Space of modular forms of level 25, weight 22, and Character 25.b

• Label: 25.22.b
• Level: $25$
• Weight: $22$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $4$
• Sturm bound: $55$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
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:			\(55\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(25, [\chi])\).

	Total	New	Old
Modular forms	56	32	24
Cusp forms	50	30	20
Eisenstein series	6	2	4

Trace form

\( 30 q - 31784210 q^{4} - 255239990 q^{6} - 63470082940 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.22.b.a	$25$	$22$	25.b	5.b	$2$	$2$	$2$	$69.869$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+12^{2}iq^{2}-64422iq^{3}+2014208q^{4}+\cdots\)
25.22.b.b	$25$	$22$	25.b	5.b	$2$	$6$	$6$	$69.869$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{17}\cdot 3^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{4})q^{2}+(-68\beta _{1}+7\beta _{4}+\cdots)q^{3}+\cdots\)
25.22.b.c	$25$	$22$	25.b	5.b	$2$	$8$	$8$	$69.869$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{2}\cdot 5^{14}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}-\beta _{5})q^{2}+(-14\beta _{4}+11\beta _{5}+\cdots)q^{3}+\cdots\)
25.22.b.d	$25$	$22$	25.b	5.b	$2$	$14$	$14$	$69.869$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{6}\cdot 5^{50}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+(-\beta _{7}+\beta _{9})q^{3}+(-1107130+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{22}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)