Space of modular forms of level 625, weight 2, and Character 625.b

• Label: 625.2.b
• Level: $625$
• Weight: $2$
• Character orbit: 625.b
• Rep. character: $\chi_{625}(624,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $125$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(125\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(625, [\chi])\).

	Total	New	Old
Modular forms	78	48	30
Cusp forms	48	32	16
Eisenstein series	30	16	14

Trace form

\( 32 q - 24 q^{4} + 4 q^{6} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(625, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
625.2.b.a	$625$	$2$	625.b	5.b	$2$	$4$	$4$	$4.991$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
625.2.b.b	$625$	$2$	625.b	5.b	$2$	$4$	$4$	$4.991$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
625.2.b.c	$625$	$2$	625.b	5.b	$2$	$8$	$8$	$4.991$	8.0.58140625.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{5}+\beta _{6})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
625.2.b.d	$625$	$2$	625.b	5.b	$2$	$16$	$16$	$4.991$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}-\beta _{10}q^{3}+(-1-\beta _{12})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(625, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(625, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)