Space of modular forms of level 7803, weight 2, and trivial character

• Label: 7803.2.a
• Level: $7803$
• Weight: $2$
• Character orbit: 7803.a
• Rep. character: $\chi_{7803}(1,\cdot)$
• Character field: $\Q$
• Dimension: $361$
• Newform subspaces: $59$
• Sturm bound: $1836$
• Trace bound: $73$

Defining parameters

Level:	\( N \)	\(=\)	\( 7803 = 3^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7803.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 59 \)
Sturm bound:			\(1836\)
Trace bound:			\(73\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7803))\).

	Total	New	Old
Modular forms	972	361	611
Cusp forms	865	361	504
Eisenstein series	107	0	107

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

\(3\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(234\)	\(84\)	\(150\)		\(208\)	\(84\)	\(124\)		\(26\)	\(0\)	\(26\)
\(+\)	\(-\)	\(-\)		\(252\)	\(96\)	\(156\)		\(225\)	\(96\)	\(129\)		\(27\)	\(0\)	\(27\)
\(-\)	\(+\)	\(-\)		\(252\)	\(96\)	\(156\)		\(225\)	\(96\)	\(129\)		\(27\)	\(0\)	\(27\)
\(-\)	\(-\)	\(+\)		\(234\)	\(85\)	\(149\)		\(207\)	\(85\)	\(122\)		\(27\)	\(0\)	\(27\)
Plus space		\(+\)		\(468\)	\(169\)	\(299\)		\(415\)	\(169\)	\(246\)		\(53\)	\(0\)	\(53\)
Minus space		\(-\)		\(504\)	\(192\)	\(312\)		\(450\)	\(192\)	\(258\)		\(54\)	\(0\)	\(54\)

Trace form

361 * q + 362 * q^4 - q^7 - 12 * q^10 - 7 * q^13 + 376 * q^16 + 5 * q^19 + 20 * q^22 + 351 * q^25 + 30 * q^28 + 16 * q^31 - 17 * q^37 - 56 * q^40 - 8 * q^43 + 12 * q^46 + 338 * q^49 - 14 * q^52 + 12 * q^55 + 32 * q^58 - 13 * q^61 + 380 * q^64 + 53 * q^67 + 80 * q^70 - 27 * q^73 + 58 * q^76 + 49 * q^79 + 32 * q^82 + 88 * q^88 + 63 * q^91 + 120 * q^94 - 31 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7803))\) 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	17
7803.2.a.a	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2q^{5}-4q^{7}+4q^{10}+\cdots\)
7803.2.a.b	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2q^{5}-q^{7}+4q^{10}+\cdots\)
7803.2.a.c	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{5}+q^{7}-4q^{10}+\cdots\)
7803.2.a.d	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.a	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+4q^{5}-q^{7}-8q^{10}+\cdots\)
7803.2.a.e	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{5}+2q^{7}+3q^{8}+4q^{10}+\cdots\)
7803.2.a.f	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7803.2.a.g	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{5}-2q^{7}+3q^{8}-4q^{10}+\cdots\)
7803.2.a.h	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}-2q^{7}+3q^{11}+2q^{13}+\cdots\)
7803.2.a.i	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			7803.2.a.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
7803.2.a.j	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			7803.2.a.j	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-4q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7803.2.a.k	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				27.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
7803.2.a.l	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			7803.2.a.j	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+4q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7803.2.a.m	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			7803.2.a.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(5\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
7803.2.a.n	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.d	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-2q^{7}-3q^{11}+2q^{13}+\cdots\)
7803.2.a.o	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.e	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{5}-2q^{7}-3q^{8}-4q^{10}+\cdots\)
7803.2.a.p	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.c	$1$	$0$	\(1\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots\)
7803.2.a.q	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.e	$1$	$1$	\(1\)	\(0\)	\(4\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{5}+2q^{7}-3q^{8}+4q^{10}+\cdots\)
7803.2.a.r	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-4q^{5}-q^{7}-8q^{10}+\cdots\)
7803.2.a.s	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.b	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}+q^{7}-4q^{10}+\cdots\)
7803.2.a.t	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓				459.2.a.b	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}-4q^{7}+4q^{10}+\cdots\)
7803.2.a.u	$7803$	$2$	7803.a	1.a	$1$	$1$	$1$	$62.307$	\(\Q\)	None	✓	✓			7803.2.a.b	$1$	$1$	\(2\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}-q^{7}+4q^{10}+\cdots\)
7803.2.a.v	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{5}) \)	None	✓				459.2.a.i	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
7803.2.a.w	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{13}) \)	None	✓				459.2.a.j	$1$	$1$	\(-1\)	\(0\)	\(5\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
7803.2.a.x	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{17}) \)	\(\Q(\sqrt{-51}) \)	✓				459.2.d.a	$2$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-1-\beta )q^{5}+(1-2\beta )q^{11}+\cdots\)
7803.2.a.y	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{17}) \)	\(\Q(\sqrt{-51}) \)	✓				459.2.d.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(1+\beta )q^{5}+(-1+2\beta )q^{11}+\cdots\)
7803.2.a.z	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{2}) \)	None	✓				459.2.f.a	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-4q^{5}-2\beta q^{7}-2\beta q^{8}-4\beta q^{10}+\cdots\)
7803.2.a.ba	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{2}) \)	None	✓				459.2.f.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{5}+2\beta q^{7}-2\beta q^{8}+4\beta q^{10}+\cdots\)
7803.2.a.bb	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{5}) \)	None	✓				459.2.a.i	$1$	$0$	\(1\)	\(0\)	\(3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+3\beta q^{7}+\cdots\)
7803.2.a.bc	$7803$	$2$	7803.a	1.a	$1$	$2$	$2$	$62.307$	\(\Q(\sqrt{13}) \)	None	✓				459.2.a.j	$1$	$1$	\(1\)	\(0\)	\(-5\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+(-3+\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
7803.2.a.bd	$7803$	$2$	7803.a	1.a	$1$	$3$	$3$	$62.307$	3.3.404.1	None	✓				459.2.a.m	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7803.2.a.be	$7803$	$2$	7803.a	1.a	$1$	$3$	$3$	$62.307$	\(\Q(\zeta_{18})^+\)	\(\Q(\sqrt{-3}) \)	✓	✓			7803.2.a.be	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-2\beta _{1}-\beta _{2})q^{7}+(-3\beta _{1}+\cdots)q^{13}+\cdots\)
7803.2.a.bf	$7803$	$2$	7803.a	1.a	$1$	$3$	$3$	$62.307$	\(\Q(\zeta_{18})^+\)	\(\Q(\sqrt{-3}) \)	✓	✓			7803.2.a.be	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(2\beta _{1}+\beta _{2})q^{7}+(-3\beta _{1}+4\beta _{2})q^{13}+\cdots\)
7803.2.a.bg	$7803$	$2$	7803.a	1.a	$1$	$3$	$3$	$62.307$	3.3.404.1	None	✓				459.2.a.m	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
7803.2.a.bh	$7803$	$2$	7803.a	1.a	$1$	$4$	$4$	$62.307$	4.4.29952.1	None	✓				459.2.d.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\)
7803.2.a.bi	$7803$	$2$	7803.a	1.a	$1$	$4$	$4$	$62.307$	4.4.29952.1	None	✓				459.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{3}q^{7}+\cdots\)
7803.2.a.bj	$7803$	$2$	7803.a	1.a	$1$	$5$	$5$	$62.307$	5.5.160801.1	None	✓	✓			7803.2.a.bj	$1$	$1$	\(-3\)	\(0\)	\(-4\)	\(1\)		$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
7803.2.a.bk	$7803$	$2$	7803.a	1.a	$1$	$5$	$5$	$62.307$	5.5.160801.1	None	✓	✓			7803.2.a.bj	$1$	$1$	\(-3\)	\(0\)	\(4\)	\(-1\)		$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
7803.2.a.bl	$7803$	$2$	7803.a	1.a	$1$	$5$	$5$	$62.307$	5.5.160801.1	None	✓	✓			7803.2.a.bj	$1$	$0$	\(3\)	\(0\)	\(-4\)	\(-1\)		$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7803.2.a.bm	$7803$	$2$	7803.a	1.a	$1$	$5$	$5$	$62.307$	5.5.160801.1	None	✓	✓			7803.2.a.bj	$1$	$0$	\(3\)	\(0\)	\(4\)	\(1\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
7803.2.a.bn	$7803$	$2$	7803.a	1.a	$1$	$6$	$6$	$62.307$	6.6.435306496.1	None	✓	✓			7803.2.a.bn	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bo	$7803$	$2$	7803.a	1.a	$1$	$6$	$6$	$62.307$	6.6.435306496.1	None	✓	✓			7803.2.a.bn	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.bp	$7803$	$2$	7803.a	1.a	$1$	$6$	$6$	$62.307$	6.6.1168184448.1	None	✓				459.2.d.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bq	$7803$	$2$	7803.a	1.a	$1$	$6$	$6$	$62.307$	6.6.1168184448.1	None	✓				459.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.br	$7803$	$2$	7803.a	1.a	$1$	$10$	$10$	$62.307$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				459.2.f.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
7803.2.a.bs	$7803$	$2$	7803.a	1.a	$1$	$10$	$10$	$62.307$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				459.2.f.b	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\beta _{6}q^{7}+\cdots\)
7803.2.a.bt	$7803$	$2$	7803.a	1.a	$1$	$12$	$12$	$62.307$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7803.2.a.bt	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bu	$7803$	$2$	7803.a	1.a	$1$	$12$	$12$	$62.307$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7803.2.a.bt	$2$	$1$	\(0\)	\(0\)	\(0\)	\(6\)		$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.bv	$7803$	$2$	7803.a	1.a	$1$	$12$	$12$	$62.307$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				459.2.f.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{11})q^{5}+\cdots\)
7803.2.a.bw	$7803$	$2$	7803.a	1.a	$1$	$12$	$12$	$62.307$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				459.2.f.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{11})q^{5}+\cdots\)
7803.2.a.bx	$7803$	$2$	7803.a	1.a	$1$	$15$	$15$	$62.307$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓		7803.2.a.bx	$1$	$1$	\(-6\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.by	$7803$	$2$	7803.a	1.a	$1$	$15$	$15$	$62.307$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓			7803.2.a.bx	$1$	$1$	\(-6\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
7803.2.a.bz	$7803$	$2$	7803.a	1.a	$1$	$15$	$15$	$62.307$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓			7803.2.a.bx	$1$	$0$	\(6\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
7803.2.a.ca	$7803$	$2$	7803.a	1.a	$1$	$15$	$15$	$62.307$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓			7803.2.a.bx	$1$	$0$	\(6\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.cb	$7803$	$2$	7803.a	1.a	$1$	$18$	$18$	$62.307$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			7803.2.a.cb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(\beta _{7}+\cdots)q^{7}+\cdots\)
7803.2.a.cc	$7803$	$2$	7803.a	1.a	$1$	$18$	$18$	$62.307$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		7803.2.a.cb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots\)
7803.2.a.cd	$7803$	$2$	7803.a	1.a	$1$	$24$	$24$	$62.307$		None	✓				459.2.l.a	$2$	$1$	\(0\)	\(0\)	\(-20\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7803.2.a.ce	$7803$	$2$	7803.a	1.a	$1$	$24$	$24$	$62.307$		None	✓				459.2.l.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-16\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7803.2.a.cf	$7803$	$2$	7803.a	1.a	$1$	$24$	$24$	$62.307$		None	✓				459.2.l.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
7803.2.a.cg	$7803$	$2$	7803.a	1.a	$1$	$24$	$24$	$62.307$		None	✓				459.2.l.a	$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7803))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7803)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(459))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2601))\)\(^{\oplus 2}\)