Space of modular forms of level 3654, weight 2, and Character 3654.g

• Label: 3654.2.g
• Level: $3654$
• Weight: $2$
• Character orbit: 3654.g
• Rep. character: $\chi_{3654}(2899,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $19$
• Sturm bound: $1440$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3654 = 2 \cdot 3^{2} \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3654.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1440\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3654, [\chi])\).

	Total	New	Old
Modular forms	736	76	660
Cusp forms	704	76	628
Eisenstein series	32	0	32

Trace form

76 * q - 76 * q^4 - 16 * q^13 + 76 * q^16 - 4 * q^22 - 8 * q^23 + 56 * q^25 - 20 * q^29 - 24 * q^34 - 4 * q^35 - 4 * q^38 + 76 * q^49 + 16 * q^52 + 4 * q^53 - 8 * q^58 + 4 * q^59 - 20 * q^62 - 76 * q^64 - 60 * q^65 + 40 * q^67 - 32 * q^71 - 64 * q^74 + 8 * q^82 + 100 * q^83 + 28 * q^86 + 4 * q^88 + 12 * q^91 + 8 * q^92 + 12 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(3654, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3654.2.g.a	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None					1218.2.g.e	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-4 q^{5}+q^{7}-i q^{8}+\cdots\)
3654.2.g.b	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None		✓			3654.2.g.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-2 q^{5}-q^{7}+i q^{8}+\cdots\)
3654.2.g.c	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None					1218.2.g.d	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-2 q^{5}+q^{7}+i q^{8}+\cdots\)
3654.2.g.d	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None					406.2.c.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-q^{5}+q^{7}-i q^{8}+\cdots\)
3654.2.g.e	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None					1218.2.g.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-q^{7}+i q^{8}-4 i q^{11}+\cdots\)
3654.2.g.f	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None					1218.2.g.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-q^{7}-i q^{8}-3 i q^{11}+\cdots\)
3654.2.g.g	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None		✓			3654.2.g.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+2 q^{5}-q^{7}+i q^{8}+\cdots\)
3654.2.g.h	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	\(\Q(\sqrt{-1}) \)	None					1218.2.g.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+4 q^{5}+q^{7}+i q^{8}+\cdots\)
3654.2.g.i	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	\(\Q(i, \sqrt{33})\)	None		✓			3654.2.g.i	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}-2q^{5}+q^{7}+\beta _{2}q^{8}+\cdots\)
3654.2.g.j	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	\(\Q(i, \sqrt{5})\)	None					1218.2.g.h	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+(-1+\beta _{3})q^{5}+q^{7}+\cdots\)
3654.2.g.k	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	\(\Q(i, \sqrt{57})\)	None					1218.2.g.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+q^{7}+\beta _{2}q^{8}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
3654.2.g.l	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	\(\Q(i, \sqrt{7})\)	None					1218.2.g.f	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+(1-\beta _{2})q^{5}-q^{7}-\beta _{1}q^{8}+\cdots\)
3654.2.g.m	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	\(\Q(i, \sqrt{33})\)	None		✓			3654.2.g.i	$2$	$0$	\(0\)	\(0\)	\(8\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+2q^{5}+q^{7}-\beta _{2}q^{8}+\cdots\)
3654.2.g.n	$3654$	$2$	3654.g	29.b	$2$	$6$	$6$	$29.177$	6.0.16516096.2	None		✓			3654.2.g.n	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}-2q^{5}-q^{7}+\beta _{1}q^{8}+\cdots\)
3654.2.g.o	$3654$	$2$	3654.g	29.b	$2$	$6$	$6$	$29.177$	6.0.399424.1	None					1218.2.g.i	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(1+\beta _{1}+\beta _{3})q^{5}-q^{7}+\cdots\)
3654.2.g.p	$3654$	$2$	3654.g	29.b	$2$	$6$	$6$	$29.177$	6.0.2611456.1	None					406.2.c.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}+(1-\beta _{2})q^{5}+q^{7}-\beta _{3}q^{8}+\cdots\)
3654.2.g.q	$3654$	$2$	3654.g	29.b	$2$	$6$	$6$	$29.177$	6.0.16516096.2	None		✓			3654.2.g.n	$2$	$0$	\(0\)	\(0\)	\(12\)	\(-6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}+2q^{5}-q^{7}+\beta _{1}q^{8}+\cdots\)
3654.2.g.r	$3654$	$2$	3654.g	29.b	$2$	$8$	$8$	$29.177$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					406.2.c.c	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-q^{4}+(-1-\beta _{2}+\beta _{6})q^{5}+\cdots\)
3654.2.g.s	$3654$	$2$	3654.g	29.b	$2$	$8$	$8$	$29.177$	8.0.12960000.1	None		✓			3654.2.g.s	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+q^{7}+\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3654, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3654, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(203, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(406, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(522, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(609, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1218, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1827, [\chi])\)\(^{\oplus 2}\)