Space of modular forms of level 25, weight 12, and Character 25.b

• Label: 25.12.b
• Level: $25$
• Weight: $12$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(30\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(25, [\chi])\).

	Total	New	Old
Modular forms	30	18	12
Cusp forms	24	16	8
Eisenstein series	6	2	4

Trace form

\( 16 q - 20338 q^{4} - 7958 q^{6} - 1029592 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.12.b.a	$25$	$12$	25.b	5.b	$2$	$2$	$2$	$19.209$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+17iq^{2}+396iq^{3}+892q^{4}-26928q^{6}+\cdots\)
25.12.b.b	$25$	$12$	25.b	5.b	$2$	$2$	$2$	$19.209$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+12iq^{2}+126iq^{3}+1472q^{4}-6048q^{6}+\cdots\)
25.12.b.c	$25$	$12$	25.b	5.b	$2$	$4$	$4$	$19.209$	\(\Q(i, \sqrt{151})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-3\beta _{3})q^{2}+(-11\beta _{1}+2^{4}\beta _{3})q^{3}+\cdots\)
25.12.b.d	$25$	$12$	25.b	5.b	$2$	$8$	$8$	$19.209$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-2\beta _{4}+\beta _{5})q^{3}+(-1389+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(25, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)