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

• Label: 2610.2.e
• Level: $2610$
• Weight: $2$
• Character orbit: 2610.e
• Rep. character: $\chi_{2610}(2089,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $11$
• Sturm bound: $1080$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2610.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1080\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	556	70	486
Cusp forms	524	70	454
Eisenstein series	32	0	32

Trace form

\( 70 q - 70 q^{4} - 8 q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2610.2.e.a	$2610$	$2$	2610.e	5.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1+2i)q^{5}+2iq^{7}+\cdots\)
2610.2.e.b	$2610$	$2$	2610.e	5.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1+2i)q^{5}+4iq^{7}+\cdots\)
2610.2.e.c	$2610$	$2$	2610.e	5.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots\)
2610.2.e.d	$2610$	$2$	2610.e	5.b	$2$	$2$	$2$	$20.841$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots\)
2610.2.e.e	$2610$	$2$	2610.e	5.b	$2$	$4$	$4$	$20.841$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2610.2.e.f	$2610$	$2$	2610.e	5.b	$2$	$4$	$4$	$20.841$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2610.2.e.g	$2610$	$2$	2610.e	5.b	$2$	$6$	$6$	$20.841$	6.0.3534400.1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{4}+(-1-\beta _{2}-\beta _{4})q^{5}+\cdots\)
2610.2.e.h	$2610$	$2$	2610.e	5.b	$2$	$10$	$10$	$20.841$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{5}q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
2610.2.e.i	$2610$	$2$	2610.e	5.b	$2$	$10$	$10$	$20.841$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2610.2.e.j	$2610$	$2$	2610.e	5.b	$2$	$14$	$14$	$20.841$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-q^{4}-\beta _{9}q^{5}+(\beta _{6}-\beta _{13})q^{7}+\cdots\)
2610.2.e.k	$2610$	$2$	2610.e	5.b	$2$	$14$	$14$	$20.841$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-q^{4}+\beta _{9}q^{5}+(\beta _{6}-\beta _{13})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2610, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(870, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1305, [\chi])\)\(^{\oplus 2}\)