Space of modular forms of level 25, weight 26, and Character 25.b

• Label: 25.26.b
• Level: $25$
• Weight: $26$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $65$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
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:			\(65\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(25, [\chi])\).

	Total	New	Old
Modular forms	66	38	28
Cusp forms	60	36	24
Eisenstein series	6	2	4

Trace form

\( 36 q - 639695442 q^{4} - 16762414838 q^{6} - 8813449216228 q^{9} + O(q^{10}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.26.b.a	$25$	$26$	25.b	5.b	$2$	$2$	$2$	$98.999$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+24iq^{2}-97902iq^{3}+33552128q^{4}+\cdots\)
25.26.b.b	$25$	$26$	25.b	5.b	$2$	$8$	$8$	$98.999$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{4}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(17\beta _{4}+158\beta _{5}+\beta _{6})q^{3}+\cdots\)
25.26.b.c	$25$	$26$	25.b	5.b	$2$	$10$	$10$	$98.999$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{29}\cdot 3^{6}\cdot 5^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(5^{2}\beta _{5}-24\beta _{6}-\beta _{7})q^{3}+\cdots\)
25.26.b.d	$25$	$26$	25.b	5.b	$2$	$16$	$16$	$98.999$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}\cdot 3^{14}\cdot 5^{66}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(23\beta _{1}+\beta _{10})q^{3}+(-21241963+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{26}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{26}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)