Space of modular forms of level 25, weight 33, and Character 25.c

• Label: 25.33.c
• Level: $25$
• Weight: $33$
• Character orbit: 25.c
• Rep. character: $\chi_{25}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $94$
• Newform subspaces: $3$
• Sturm bound: $82$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(82\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(25, [\chi])\).

	Total	New	Old
Modular forms	166	98	68
Cusp forms	154	94	60
Eisenstein series	12	4	8

Trace form

\( 94 q + 2 q^{2} + 2792232 q^{3} + 1290952902468 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8} + O(q^{10}) \)

Decomposition of \(S_{33}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.33.c.a	$25$	$33$	25.c	5.c	$4$	$20$	$10$	$162.167$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{97}\cdot 3^{24}\cdot 5^{48}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(92\beta _{13}+\beta _{16})q^{3}+(1560690866\beta _{9}+\cdots)q^{4}+\cdots\)
25.33.c.b	$25$	$33$	25.c	5.c	$4$	$30$	$15$	$162.167$		None		$2$	$0$	\(2\)	\(2792232\)	\(0\)	\(-21\!\cdots\!48\)		$\mathrm{SU}(2)[C_{4}]$
25.33.c.c	$25$	$33$	25.c	5.c	$4$	$44$	$22$	$162.167$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{33}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{33}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{33}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)