Space of modular forms of level 425, weight 2, and Character 425.c

• Label: 425.2.c
• Level: $425$
• Weight: $2$
• Character orbit: 425.c
• Rep. character: $\chi_{425}(424,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $90$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(90\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(425, [\chi])\).

	Total	New	Old
Modular forms	52	28	24
Cusp forms	40	24	16
Eisenstein series	12	4	8

Trace form

24 * q - 8 * q^4 + 28 * q^9 - 24 * q^16 - 24 * q^19 - 20 * q^21 + 4 * q^26 - 48 * q^34 + 4 * q^36 + 20 * q^49 + 16 * q^51 - 8 * q^59 + 88 * q^64 - 16 * q^66 - 48 * q^69 - 24 * q^76 + 16 * q^81 + 12 * q^84 + 8 * q^86 + 8 * q^89 + 64 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
425.2.c.a	$425$	$2$	425.c	85.c	$2$	$6$	$6$	$3.394$	6.0.350464.1	None					85.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
425.2.c.b	$425$	$2$	425.c	85.c	$2$	$6$	$6$	$3.394$	6.0.350464.1	None					85.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
425.2.c.c	$425$	$2$	425.c	85.c	$2$	$12$	$12$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		425.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)