Space of modular forms of level 25, weight 20, and Character 25.b

• Label: 25.20.b
• Level: $25$
• Weight: $20$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $50$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 20 \)
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:			\(50\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(25, [\chi])\).

	Total	New	Old
Modular forms	50	30	20
Cusp forms	44	28	16
Eisenstein series	6	2	4

Trace form

\( 28 q - 7244274 q^{4} - 25838294 q^{6} - 13248392296 q^{9} + O(q^{10}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.20.b.a	$25$	$20$	25.b	5.b	$2$	$2$	$2$	$57.204$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+228iq^{2}-25326iq^{3}+316352q^{4}+\cdots\)
25.20.b.b	$25$	$20$	25.b	5.b	$2$	$6$	$6$	$57.204$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 3^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(92\beta _{1}-18\beta _{2}+13\beta _{4}+\cdots)q^{3}+\cdots\)
25.20.b.c	$25$	$20$	25.b	5.b	$2$	$8$	$8$	$57.204$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{4}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(14\beta _{2}+\beta _{3}-\beta _{6})q^{3}+(-521248+\cdots)q^{4}+\cdots\)
25.20.b.d	$25$	$20$	25.b	5.b	$2$	$12$	$12$	$57.204$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}\cdot 3^{6}\cdot 5^{36}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(8\beta _{6}+\beta _{8})q^{3}+(-387^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{20}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{20}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)