Space of modular forms of level 425, weight 4, and Character 425.c

• Label: 425.4.c
• Level: $425$
• Weight: $4$
• Character orbit: 425.c
• Rep. character: $\chi_{425}(424,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $7$
• Sturm bound: $180$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(180\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

	Total	New	Old
Modular forms	140	84	56
Cusp forms	128	80	48
Eisenstein series	12	4	8

Trace form

80 * q - 340 * q^4 + 660 * q^9 + 1812 * q^16 + 180 * q^19 + 92 * q^26 + 466 * q^34 - 3268 * q^36 + 4272 * q^49 + 950 * q^51 - 1408 * q^59 - 6036 * q^64 + 4932 * q^66 + 1064 * q^69 - 5844 * q^76 + 5112 * q^81 - 4156 * q^84 + 104 * q^86 - 5724 * q^89 + 9016 * q^94

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
425.4.c.a	$425$	$4$	425.c	85.c	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None					85.4.d.a	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-8 q^{3}+7 q^{4}-8 i q^{6}-14 q^{7}+\cdots\)
425.4.c.b	$425$	$4$	425.c	85.c	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None					85.4.d.a	$2$	$0$	\(0\)	\(16\)	\(0\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+8 q^{3}+7 q^{4}+8 i q^{6}+14 q^{7}+\cdots\)
425.4.c.c	$425$	$4$	425.c	85.c	$2$	$8$	$8$	$25.076$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					17.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{4}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.c.d	$425$	$4$	425.c	85.c	$2$	$8$	$8$	$25.076$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			425.4.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{1}q^{3}+7q^{4}+\beta _{6}q^{6}+(-4\beta _{1}+\cdots)q^{7}+\cdots\)
425.4.c.e	$425$	$4$	425.c	85.c	$2$	$16$	$16$	$25.076$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					85.4.d.b	$2$	$0$	\(0\)	\(-36\)	\(0\)	\(-76\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+(-6+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.c.f	$425$	$4$	425.c	85.c	$2$	$16$	$16$	$25.076$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					85.4.d.b	$2$	$0$	\(0\)	\(36\)	\(0\)	\(76\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+(-6+\beta _{2})q^{4}+\cdots\)
425.4.c.g	$425$	$4$	425.c	85.c	$2$	$28$	$28$	$25.076$		None		✓	✓		425.4.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)