Space of modular forms of level 7406, weight 2, and trivial character

• Label: 7406.2.a
• Level: $7406$
• Weight: $2$
• Character orbit: 7406.a
• Rep. character: $\chi_{7406}(1,\cdot)$
• Character field: $\Q$
• Dimension: $252$
• Newform subspaces: $48$
• Sturm bound: $2208$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7406.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(2208\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7406))\).

	Total	New	Old
Modular forms	1152	252	900
Cusp forms	1057	252	805
Eisenstein series	95	0	95

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

\(2\)	\(7\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(132\)	\(28\)	\(104\)		\(121\)	\(28\)	\(93\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(154\)	\(36\)	\(118\)		\(142\)	\(36\)	\(106\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(156\)	\(38\)	\(118\)		\(144\)	\(38\)	\(106\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(134\)	\(25\)	\(109\)		\(122\)	\(25\)	\(97\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(144\)	\(32\)	\(112\)		\(132\)	\(32\)	\(100\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(144\)	\(30\)	\(114\)		\(132\)	\(30\)	\(102\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(144\)	\(22\)	\(122\)		\(132\)	\(22\)	\(110\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(144\)	\(41\)	\(103\)		\(132\)	\(41\)	\(91\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(554\)	\(105\)	\(449\)		\(507\)	\(105\)	\(402\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(598\)	\(147\)	\(451\)		\(550\)	\(147\)	\(403\)		\(48\)	\(0\)	\(48\)

Trace form

252 * q - 2 * q^2 + 2 * q^3 + 252 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 248 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^13 + 2 * q^14 + 16 * q^15 + 252 * q^16 + 4 * q^17 - 6 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 - 2 * q^24 + 272 * q^25 - 2 * q^26 + 20 * q^27 + 4 * q^29 + 20 * q^31 - 2 * q^32 - 8 * q^34 + 2 * q^35 + 248 * q^36 + 8 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 + 2 * q^42 - 6 * q^45 + 12 * q^47 + 2 * q^48 + 252 * q^49 - 2 * q^50 - 20 * q^51 + 6 * q^52 + 12 * q^53 - 20 * q^54 + 16 * q^55 + 2 * q^56 + 4 * q^57 + 8 * q^58 + 6 * q^59 + 16 * q^60 - 22 * q^61 + 20 * q^62 + 12 * q^63 + 252 * q^64 - 36 * q^65 + 16 * q^66 + 4 * q^67 + 4 * q^68 + 2 * q^70 + 32 * q^71 - 6 * q^72 + 8 * q^73 + 12 * q^74 + 14 * q^75 + 6 * q^76 - 12 * q^77 + 16 * q^78 + 24 * q^79 + 2 * q^80 + 272 * q^81 - 16 * q^82 - 10 * q^83 - 2 * q^84 - 44 * q^85 - 16 * q^86 - 36 * q^87 + 34 * q^90 - 6 * q^91 - 32 * q^93 - 20 * q^94 + 16 * q^95 - 2 * q^96 + 4 * q^97 - 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7406))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	23
7406.2.a.a	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓				14.2.a.a	$1$	$2$	\(-1\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
7406.2.a.b	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓	✓			7406.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
7406.2.a.c	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓	✓			7406.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-4q^{11}+\cdots\)
7406.2.a.d	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓				322.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
7406.2.a.e	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓				322.2.a.b	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
7406.2.a.f	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓				322.2.a.c	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{7}+\cdots\)
7406.2.a.g	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓	✓			7406.2.a.g	$1$	$1$	\(1\)	\(-1\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7406.2.a.h	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓	✓			7406.2.a.g	$1$	$0$	\(1\)	\(-1\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
7406.2.a.i	$7406$	$2$	7406.a	1.a	$1$	$1$	$1$	$59.137$	\(\Q\)	None	✓				322.2.a.d	$1$	$1$	\(1\)	\(2\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{7}+\cdots\)
7406.2.a.j	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{5}) \)	None	✓				322.2.a.e	$1$	$1$	\(-2\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
7406.2.a.k	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{13}) \)	None	✓	✓			7406.2.a.k	$1$	$0$	\(-2\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
7406.2.a.l	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{13}) \)	None	✓	✓			7406.2.a.k	$1$	$1$	\(-2\)	\(-1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
7406.2.a.m	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{6}) \)	None	✓	✓			7406.2.a.m	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+\beta q^{5}-\beta q^{6}-q^{7}+\cdots\)
7406.2.a.n	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{6}) \)	None	✓	✓			7406.2.a.m	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots\)
7406.2.a.o	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{5}) \)	None	✓	✓			7406.2.a.o	$1$	$1$	\(-2\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
7406.2.a.p	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{5}) \)	None	✓	✓			7406.2.a.o	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
7406.2.a.q	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{2}) \)	None	✓	✓			7406.2.a.q	$1$	$1$	\(-2\)	\(4\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2\beta q^{5}-2q^{6}+\cdots\)
7406.2.a.r	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{2}) \)	None	✓	✓			7406.2.a.q	$1$	$0$	\(-2\)	\(4\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2\beta q^{5}-2q^{6}+\cdots\)
7406.2.a.s	$7406$	$2$	7406.a	1.a	$1$	$2$	$2$	$59.137$	\(\Q(\sqrt{3}) \)	None	✓				322.2.a.f	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
7406.2.a.t	$7406$	$2$	7406.a	1.a	$1$	$3$	$3$	$59.137$	3.3.148.1	None	✓	✓			7406.2.a.t	$1$	$1$	\(3\)	\(-2\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
7406.2.a.u	$7406$	$2$	7406.a	1.a	$1$	$3$	$3$	$59.137$	3.3.148.1	None	✓	✓			7406.2.a.t	$1$	$0$	\(3\)	\(-2\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots\)
7406.2.a.v	$7406$	$2$	7406.a	1.a	$1$	$3$	$3$	$59.137$	3.3.1509.1	None	✓	✓			7406.2.a.v	$1$	$0$	\(3\)	\(-1\)	\(-4\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
7406.2.a.w	$7406$	$2$	7406.a	1.a	$1$	$3$	$3$	$59.137$	3.3.1509.1	None	✓	✓			7406.2.a.v	$1$	$1$	\(3\)	\(-1\)	\(4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.x	$7406$	$2$	7406.a	1.a	$1$	$3$	$3$	$59.137$	3.3.316.1	None	✓				322.2.a.g	$1$	$0$	\(3\)	\(2\)	\(-4\)	\(3\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
7406.2.a.y	$7406$	$2$	7406.a	1.a	$1$	$4$	$4$	$59.137$	\(\Q(\zeta_{24})^+\)	None	✓	✓			7406.2.a.y	$1$	$1$	\(-4\)	\(-4\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7406.2.a.z	$7406$	$2$	7406.a	1.a	$1$	$4$	$4$	$59.137$	\(\Q(\zeta_{24})^+\)	None	✓	✓			7406.2.a.y	$1$	$0$	\(-4\)	\(-4\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7406.2.a.ba	$7406$	$2$	7406.a	1.a	$1$	$4$	$4$	$59.137$	4.4.449797.1	None	✓	✓			7406.2.a.ba	$1$	$1$	\(4\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
7406.2.a.bb	$7406$	$2$	7406.a	1.a	$1$	$4$	$4$	$59.137$	\(\Q(\sqrt{10 +4 \sqrt{2}})\)	None	✓	✓			7406.2.a.bb	$1$	$1$	\(4\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
7406.2.a.bc	$7406$	$2$	7406.a	1.a	$1$	$4$	$4$	$59.137$	\(\Q(\sqrt{10 +4 \sqrt{2}})\)	None	✓	✓			7406.2.a.bb	$1$	$0$	\(4\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
7406.2.a.bd	$7406$	$2$	7406.a	1.a	$1$	$4$	$4$	$59.137$	4.4.449797.1	None	✓	✓			7406.2.a.ba	$1$	$0$	\(4\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
7406.2.a.be	$7406$	$2$	7406.a	1.a	$1$	$5$	$5$	$59.137$	\(\Q(\zeta_{22})^+\)	None	✓				322.2.i.b	$1$	$1$	\(-5\)	\(-3\)	\(-4\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
7406.2.a.bf	$7406$	$2$	7406.a	1.a	$1$	$5$	$5$	$59.137$	\(\Q(\zeta_{22})^+\)	None	✓				322.2.i.b	$1$	$1$	\(-5\)	\(-3\)	\(4\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+q^{4}+(2+\cdots)q^{5}+\cdots\)
7406.2.a.bg	$7406$	$2$	7406.a	1.a	$1$	$5$	$5$	$59.137$	\(\Q(\zeta_{22})^+\)	None	✓				322.2.i.a	$1$	$1$	\(-5\)	\(4\)	\(-3\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
7406.2.a.bh	$7406$	$2$	7406.a	1.a	$1$	$5$	$5$	$59.137$	\(\Q(\zeta_{22})^+\)	None	✓				322.2.i.a	$1$	$1$	\(-5\)	\(4\)	\(3\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
7406.2.a.bi	$7406$	$2$	7406.a	1.a	$1$	$6$	$6$	$59.137$	6.6.596217024.1	None	✓	✓			7406.2.a.bi	$1$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7406.2.a.bj	$7406$	$2$	7406.a	1.a	$1$	$6$	$6$	$59.137$	6.6.596217024.1	None	✓	✓	✓		7406.2.a.bi	$1$	$1$	\(-6\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
7406.2.a.bk	$7406$	$2$	7406.a	1.a	$1$	$6$	$6$	$59.137$	6.6.84770496.1	None	✓	✓			7406.2.a.bk	$1$	$1$	\(6\)	\(2\)	\(-4\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
7406.2.a.bl	$7406$	$2$	7406.a	1.a	$1$	$6$	$6$	$59.137$	6.6.84770496.1	None	✓	✓			7406.2.a.bk	$1$	$0$	\(6\)	\(2\)	\(4\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)
7406.2.a.bm	$7406$	$2$	7406.a	1.a	$1$	$8$	$8$	$59.137$	8.8.6120603648.1	None	✓	✓			7406.2.a.bm	$1$	$1$	\(8\)	\(0\)	\(-8\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
7406.2.a.bn	$7406$	$2$	7406.a	1.a	$1$	$8$	$8$	$59.137$	8.8.6120603648.1	None	✓	✓			7406.2.a.bm	$1$	$0$	\(8\)	\(0\)	\(8\)	\(-8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
7406.2.a.bo	$7406$	$2$	7406.a	1.a	$1$	$10$	$10$	$59.137$	10.10.\(\cdots\).1	None	✓		✓		322.2.i.c	$1$	$1$	\(10\)	\(-9\)	\(-3\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{9})q^{5}+\cdots\)
7406.2.a.bp	$7406$	$2$	7406.a	1.a	$1$	$10$	$10$	$59.137$	10.10.\(\cdots\).1	None	✓		✓		322.2.i.c	$1$	$1$	\(10\)	\(-9\)	\(3\)	\(10\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7406.2.a.bq	$7406$	$2$	7406.a	1.a	$1$	$12$	$12$	$59.137$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		7406.2.a.bq	$1$	$1$	\(-12\)	\(0\)	\(0\)	\(-12\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.br	$7406$	$2$	7406.a	1.a	$1$	$12$	$12$	$59.137$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7406.2.a.bq	$1$	$0$	\(-12\)	\(0\)	\(0\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.bs	$7406$	$2$	7406.a	1.a	$1$	$20$	$20$	$59.137$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		322.2.i.e	$1$	$0$	\(-20\)	\(1\)	\(-1\)	\(-20\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{12}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.bt	$7406$	$2$	7406.a	1.a	$1$	$20$	$20$	$59.137$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		322.2.i.e	$1$	$0$	\(-20\)	\(1\)	\(1\)	\(20\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{12}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.bu	$7406$	$2$	7406.a	1.a	$1$	$20$	$20$	$59.137$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		322.2.i.d	$1$	$0$	\(20\)	\(11\)	\(-1\)	\(-20\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{12}q^{5}+\cdots\)
7406.2.a.bv	$7406$	$2$	7406.a	1.a	$1$	$20$	$20$	$59.137$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		322.2.i.d	$1$	$0$	\(20\)	\(11\)	\(1\)	\(20\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{12}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7406))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7406)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3703))\)\(^{\oplus 2}\)