Space of modular forms of level 8379, weight 2, and trivial character

• Label: 8379.2.a
• Level: $8379$
• Weight: $2$
• Character orbit: 8379.a
• Rep. character: $\chi_{8379}(1,\cdot)$
• Character field: $\Q$
• Dimension: $308$
• Newform subspaces: $76$
• Sturm bound: $2240$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 8379 = 3^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8379.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 76 \)
Sturm bound:			\(2240\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8379))\).

	Total	New	Old
Modular forms	1152	308	844
Cusp forms	1089	308	781
Eisenstein series	63	0	63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(136\)	\(28\)	\(108\)		\(129\)	\(28\)	\(101\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)		\(152\)	\(36\)	\(116\)		\(144\)	\(36\)	\(108\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)		\(148\)	\(36\)	\(112\)		\(140\)	\(36\)	\(104\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)		\(140\)	\(24\)	\(116\)		\(132\)	\(24\)	\(108\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)		\(152\)	\(46\)	\(106\)		\(144\)	\(46\)	\(98\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)		\(136\)	\(42\)	\(94\)		\(128\)	\(42\)	\(86\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)		\(140\)	\(45\)	\(95\)		\(132\)	\(45\)	\(87\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)		\(148\)	\(51\)	\(97\)		\(140\)	\(51\)	\(89\)		\(8\)	\(0\)	\(8\)
Plus space			\(+\)		\(552\)	\(139\)	\(413\)		\(521\)	\(139\)	\(382\)		\(31\)	\(0\)	\(31\)
Minus space			\(-\)		\(600\)	\(169\)	\(431\)		\(568\)	\(169\)	\(399\)		\(32\)	\(0\)	\(32\)

Trace form

308 * q - q^2 + 307 * q^4 + 3 * q^5 - 9 * q^8 - 2 * q^10 - 3 * q^11 + 6 * q^13 + 289 * q^16 + 13 * q^17 - 2 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 + 335 * q^25 - 2 * q^26 + 12 * q^29 - 4 * q^31 + 11 * q^32 + 18 * q^34 - 8 * q^37 + 3 * q^38 + 30 * q^40 + 16 * q^41 - 11 * q^43 - 30 * q^44 - 8 * q^46 + 7 * q^47 + q^50 + 42 * q^52 + 26 * q^53 - 33 * q^55 + 62 * q^58 - 22 * q^59 - 5 * q^61 - 36 * q^62 + 293 * q^64 + 60 * q^65 + 24 * q^67 - 24 * q^68 - 2 * q^71 - 3 * q^73 + 26 * q^74 - 5 * q^76 - 24 * q^79 - 50 * q^80 + 74 * q^82 + 12 * q^83 + 33 * q^85 + 48 * q^86 + 96 * q^88 + 38 * q^89 - 8 * q^92 + 36 * q^94 - 9 * q^95 + 46 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8379))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	19
8379.2.a.a	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				133.2.f.a	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{5}+6q^{10}-4q^{11}+\cdots\)
8379.2.a.b	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.j.a	$1$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-4q^{11}+\cdots\)
8379.2.a.c	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.j.a	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-4q^{11}+\cdots\)
8379.2.a.d	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				133.2.f.a	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+3q^{5}-6q^{10}-4q^{11}+\cdots\)
8379.2.a.e	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				57.2.a.c	$1$	$2$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
8379.2.a.f	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				1197.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}-2q^{11}+6q^{13}+\cdots\)
8379.2.a.g	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+2q^{11}+4q^{13}+\cdots\)
8379.2.a.h	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.j.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{5}+3q^{11}+2q^{13}+4q^{16}+\cdots\)
8379.2.a.i	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.j.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+2q^{5}+3q^{11}-2q^{13}+4q^{16}+\cdots\)
8379.2.a.j	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				19.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
8379.2.a.k	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				2793.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
8379.2.a.l	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}+2q^{11}-q^{16}+\cdots\)
8379.2.a.m	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				1197.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}+2q^{11}+6q^{13}+\cdots\)
8379.2.a.n	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				2793.2.a.d	$1$	$1$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
8379.2.a.o	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				399.2.a.b	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
8379.2.a.p	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				57.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}-q^{11}+\cdots\)
8379.2.a.q	$8379$	$2$	8379.a	1.a	$1$	$1$	$1$	$66.907$	\(\Q\)	None	✓				57.2.a.b	$1$	$0$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+3q^{11}+\cdots\)
8379.2.a.r	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				2793.2.a.s	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
8379.2.a.s	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				2793.2.a.s	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
8379.2.a.t	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				2793.2.a.t	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
8379.2.a.u	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				2793.2.a.t	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
8379.2.a.v	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				1197.2.a.f	$1$	$1$	\(-2\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2q^{5}+\cdots\)
8379.2.a.w	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{5}) \)	None	✓				133.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
8379.2.a.x	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{3}) \)	None	✓				1197.2.j.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-2q^{4}+\beta q^{11}-2q^{13}+4q^{16}+\beta q^{17}+\cdots\)
8379.2.a.y	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{3}) \)	None	✓				1197.2.j.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-2q^{4}-\beta q^{11}+2q^{13}+4q^{16}+\beta q^{17}+\cdots\)
8379.2.a.z	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				133.2.f.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2\beta q^{5}-2\beta q^{8}-4q^{10}+(3+\cdots)q^{11}+\cdots\)
8379.2.a.ba	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				133.2.f.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+2\beta q^{5}-2\beta q^{8}+4q^{10}+(3+\cdots)q^{11}+\cdots\)
8379.2.a.bb	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{3}) \)	None	✓				1197.2.j.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots\)
8379.2.a.bc	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{3}) \)	None	✓				2793.2.a.q	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-2\beta q^{13}+\cdots\)
8379.2.a.bd	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{3}) \)	None	✓				2793.2.a.q	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}+2\beta q^{13}+\cdots\)
8379.2.a.be	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{3}) \)	None	✓				1197.2.j.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots\)
8379.2.a.bf	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{13}) \)	None	✓				133.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}-3q^{5}+3q^{8}-3\beta q^{10}+\cdots\)
8379.2.a.bg	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				1197.2.a.f	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bh	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				399.2.j.c	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
8379.2.a.bi	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				133.2.f.c	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots\)
8379.2.a.bj	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				2793.2.a.m	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bk	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				2793.2.a.m	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
8379.2.a.bl	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				133.2.f.c	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(3+\beta )q^{8}+\cdots\)
8379.2.a.bm	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{2}) \)	None	✓				399.2.j.c	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
8379.2.a.bn	$8379$	$2$	8379.a	1.a	$1$	$2$	$2$	$66.907$	\(\Q(\sqrt{5}) \)	None	✓				133.2.a.a	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
8379.2.a.bo	$8379$	$2$	8379.a	1.a	$1$	$3$	$3$	$66.907$	3.3.229.1	None	✓				133.2.a.d	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8379.2.a.bp	$8379$	$2$	8379.a	1.a	$1$	$3$	$3$	$66.907$	3.3.148.1	None	✓				399.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
8379.2.a.bq	$8379$	$2$	8379.a	1.a	$1$	$3$	$3$	$66.907$	3.3.404.1	None	✓				399.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.br	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.1957.1	None	✓				399.2.j.d	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8379.2.a.bs	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	\(\Q(\zeta_{24})^+\)	None	✓				1197.2.a.n	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots\)
8379.2.a.bt	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.1957.1	None	✓				399.2.j.d	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.bu	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.5744.1	None	✓				931.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(-2+\cdots)q^{5}+\cdots\)
8379.2.a.bv	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.5744.1	None	✓				931.2.a.l	$1$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+(2+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.bw	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	\(\Q(\sqrt{18 +2 \sqrt{33}})\)	None	✓				171.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.bx	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				399.2.j.f	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-1+2\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.by	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	\(\Q(\sqrt{22 +2 \sqrt{5}})\)	None	✓				399.2.j.f	$1$	$1$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{4}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.bz	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.23301.1	None	✓				399.2.j.e	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(2-\beta _{2})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.ca	$8379$	$2$	8379.a	1.a	$1$	$4$	$4$	$66.907$	4.4.23301.1	None	✓				399.2.j.e	$1$	$0$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(2-\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
8379.2.a.cb	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.368464.1	None	✓				399.2.a.g	$1$	$0$	\(-3\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8379.2.a.cc	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.1244416.1	None	✓				2793.2.a.bf	$1$	$1$	\(-3\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
8379.2.a.cd	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.1244416.1	None	✓				2793.2.a.bf	$1$	$0$	\(-3\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
8379.2.a.ce	$8379$	$2$	8379.a	1.a	$1$	$5$	$5$	$66.907$	5.5.1240016.1	None	✓				399.2.a.f	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1+\beta _{4})q^{4}+\beta _{2}q^{5}+(\beta _{2}+\cdots)q^{8}+\cdots\)
8379.2.a.cf	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.39110656.1	None	✓				2793.2.a.bk	$1$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(2-\beta _{1}+\beta _{3})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.cg	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.39110656.1	None	✓				2793.2.a.bk	$1$	$1$	\(-2\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(2-\beta _{1}+\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8379.2.a.ch	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.12730624.1	None	✓				1197.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
8379.2.a.ci	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.5163008.1	None	✓				2793.2.a.bi	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots\)
8379.2.a.cj	$8379$	$2$	8379.a	1.a	$1$	$6$	$6$	$66.907$	6.6.5163008.1	None	✓				2793.2.a.bi	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\beta _{5}q^{5}+\cdots\)
8379.2.a.ck	$8379$	$2$	8379.a	1.a	$1$	$7$	$7$	$66.907$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		133.2.f.d	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1+\beta _{3}-\beta _{5})q^{4}+\beta _{6}q^{5}+\cdots\)
8379.2.a.cl	$8379$	$2$	8379.a	1.a	$1$	$7$	$7$	$66.907$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				133.2.f.d	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1+\beta _{3}-\beta _{5})q^{4}-\beta _{6}q^{5}+\cdots\)
8379.2.a.cm	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.\(\cdots\).2	None	✓				1197.2.j.n	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
8379.2.a.cn	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.8446345216.1	None	✓	✓			8379.2.a.cn	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}-\beta _{5}q^{4}-\beta _{7}q^{5}-\beta _{2}q^{8}+\cdots\)
8379.2.a.co	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.8446345216.1	None	✓	✓			8379.2.a.cn	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}-\beta _{5}q^{4}+\beta _{7}q^{5}-\beta _{2}q^{8}+\cdots\)
8379.2.a.cp	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	8.8.\(\cdots\).2	None	✓				1197.2.j.n	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
8379.2.a.cq	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		399.2.j.g	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots\)
8379.2.a.cr	$8379$	$2$	8379.a	1.a	$1$	$8$	$8$	$66.907$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				399.2.j.g	$1$	$0$	\(0\)	\(0\)	\(5\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
8379.2.a.cs	$8379$	$2$	8379.a	1.a	$1$	$10$	$10$	$66.907$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		931.2.a.p	$1$	$1$	\(2\)	\(0\)	\(-16\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{9})q^{5}+\cdots\)
8379.2.a.ct	$8379$	$2$	8379.a	1.a	$1$	$10$	$10$	$66.907$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		931.2.a.p	$1$	$0$	\(2\)	\(0\)	\(16\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+\beta _{9})q^{5}+\cdots\)
8379.2.a.cu	$8379$	$2$	8379.a	1.a	$1$	$12$	$12$	$66.907$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				1197.2.j.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
8379.2.a.cv	$8379$	$2$	8379.a	1.a	$1$	$12$	$12$	$66.907$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		1197.2.j.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
8379.2.a.cw	$8379$	$2$	8379.a	1.a	$1$	$20$	$20$	$66.907$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		8379.2.a.cw	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
8379.2.a.cx	$8379$	$2$	8379.a	1.a	$1$	$20$	$20$	$66.907$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		8379.2.a.cw	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8379))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8379)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1197))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2793))\)\(^{\oplus 2}\)