Space of modular forms of level 2610, weight 2, and Character 2610.f

• Label: 2610.2.f
• Level: $2610$
• Weight: $2$
• Character orbit: 2610.f
• Rep. character: $\chi_{2610}(811,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $10$
• Sturm bound: $1080$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2610.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1080\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2610, [\chi])\).

	Total	New	Old
Modular forms	556	50	506
Cusp forms	524	50	474
Eisenstein series	32	0	32

Trace form

50 * q - 50 * q^4 + 2 * q^5 - 4 * q^13 + 50 * q^16 - 2 * q^20 - 12 * q^22 - 40 * q^23 + 50 * q^25 - 10 * q^29 + 8 * q^34 + 12 * q^35 + 12 * q^38 + 94 * q^49 + 4 * q^52 + 12 * q^53 - 20 * q^58 + 20 * q^59 + 4 * q^62 - 50 * q^64 - 16 * q^65 + 48 * q^67 - 56 * q^71 + 4 * q^74 + 2 * q^80 + 24 * q^82 + 88 * q^83 - 4 * q^86 + 12 * q^88 - 16 * q^91 + 40 * q^92 + 8 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(2610, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2610.2.f.a	$2610$	$2$	2610.f	29.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None					870.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-q^{5}-2 q^{7}+i q^{8}+\cdots\)
2610.2.f.b	$2610$	$2$	2610.f	29.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None					870.2.f.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-q^{5}-2 q^{7}-i q^{8}+\cdots\)
2610.2.f.c	$2610$	$2$	2610.f	29.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None					290.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+q^{5}+4 q^{7}-i q^{8}+\cdots\)
2610.2.f.d	$2610$	$2$	2610.f	29.b	$2$	$4$	$4$	$20.841$	\(\Q(i, \sqrt{5})\)	None					290.2.c.c	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}-q^{5}-\beta _{2}q^{7}-\beta _{3}q^{8}+\cdots\)
2610.2.f.e	$2610$	$2$	2610.f	29.b	$2$	$4$	$4$	$20.841$	\(\Q(i, \sqrt{29})\)	None					290.2.c.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+q^{5}+(-3+\beta _{3})q^{7}+\cdots\)
2610.2.f.f	$2610$	$2$	2610.f	29.b	$2$	$4$	$4$	$20.841$	\(\Q(i, \sqrt{5})\)	None					870.2.f.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+q^{5}+(1-\beta _{3})q^{7}-\beta _{1}q^{8}+\cdots\)
2610.2.f.g	$2610$	$2$	2610.f	29.b	$2$	$6$	$6$	$20.841$	6.0.350464.1	None					870.2.f.e	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}-q^{5}-\beta _{1}q^{7}-\beta _{2}q^{8}+\cdots\)
2610.2.f.h	$2610$	$2$	2610.f	29.b	$2$	$6$	$6$	$20.841$	6.0.153664.1	None					870.2.f.d	$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+q^{5}+(1-\beta _{5})q^{7}-\beta _{2}q^{8}+\cdots\)
2610.2.f.i	$2610$	$2$	2610.f	29.b	$2$	$10$	$10$	$20.841$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			2610.2.f.i	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}-q^{5}+\beta _{1}q^{7}-\beta _{4}q^{8}+\cdots\)
2610.2.f.j	$2610$	$2$	2610.f	29.b	$2$	$10$	$10$	$20.841$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			2610.2.f.i	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}+q^{5}+\beta _{1}q^{7}-\beta _{4}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2610, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2610, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(522, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(870, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1305, [\chi])\)\(^{\oplus 2}\)