Space of modular forms of level 25, weight 32, and Character 25.b

• Label: 25.32.b
• Level: $25$
• Weight: $32$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(25, [\chi])\).

	Total	New	Old
Modular forms	80	48	32
Cusp forms	74	46	28
Eisenstein series	6	2	4

Trace form

\( 46 q - 49299449778 q^{4} - 875743077398 q^{6} - 10455028033665802 q^{9} + O(q^{10}) \)

Decomposition of \(S_{32}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.32.b.a	$25$	$32$	25.b	5.b	$2$	$4$	$4$	$152.193$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1998\beta _{1}+\beta _{2})q^{2}+(-868158\beta _{1}+\cdots)q^{3}+\cdots\)
25.32.b.b	$25$	$32$	25.b	5.b	$2$	$10$	$10$	$152.193$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{36}\cdot 3^{10}\cdot 5^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-35\beta _{5}-867\beta _{6}+\beta _{7}+\cdots)q^{3}+\cdots\)
25.32.b.c	$25$	$32$	25.b	5.b	$2$	$12$	$12$	$152.193$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{61}\cdot 3^{10}\cdot 5^{36}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(143\beta _{1}-235\beta _{7}-\beta _{8})q^{3}+\cdots\)
25.32.b.d	$25$	$32$	25.b	5.b	$2$	$20$	$20$	$152.193$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{80}\cdot 3^{22}\cdot 5^{110}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-11\beta _{1}+\beta _{11})q^{3}+(-1026979481+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{32}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{32}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{32}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)