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

• Label: 425.2.e
• Level: $425$
• Weight: $2$
• Character orbit: 425.e
• Rep. character: $\chi_{425}(251,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $52$
• Newform subspaces: $6$
• Sturm bound: $90$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(90\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	100	64	36
Cusp forms	76	52	24
Eisenstein series	24	12	12

Trace form

52 * q + 4 * q^3 - 44 * q^4 - 4 * q^6 - 8 * q^11 + 8 * q^12 + 28 * q^14 + 12 * q^16 - 12 * q^17 - 28 * q^18 - 20 * q^22 - 12 * q^23 + 32 * q^24 + 4 * q^27 - 4 * q^28 - 16 * q^29 - 12 * q^31 + 16 * q^33 + 44 * q^34 - 12 * q^37 - 24 * q^38 - 8 * q^41 + 32 * q^44 + 28 * q^46 + 48 * q^47 + 20 * q^48 - 16 * q^51 + 56 * q^52 - 56 * q^54 - 104 * q^56 - 36 * q^58 - 20 * q^61 - 40 * q^62 - 12 * q^63 - 12 * q^64 + 8 * q^67 + 40 * q^68 - 48 * q^69 - 40 * q^71 - 20 * q^72 + 48 * q^73 - 40 * q^74 + 92 * q^78 - 4 * q^79 - 28 * q^81 - 40 * q^82 + 56 * q^84 + 104 * q^86 + 72 * q^88 - 32 * q^89 + 24 * q^91 + 16 * q^92 + 28 * q^96 - 4 * q^97 - 44 * q^98 + 36 * q^99

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.e.a	$425$	$2$	425.e	17.c	$4$	$2$	$1$	$3.394$	\(\Q(\sqrt{-1}) \)	None					85.2.j.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+i q^{2}+(-i-1)q^{3}+q^{4}+(-i+1)q^{6}+\cdots\)
425.2.e.b	$425$	$2$	425.e	17.c	$4$	$2$	$1$	$3.394$	\(\Q(\sqrt{-1}) \)	None					85.2.j.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-i q^{2}+(i+1)q^{3}+q^{4}+(-i+1)q^{6}+\cdots\)
425.2.e.c	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			425.2.e.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
425.2.e.d	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					85.2.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}+(\beta _{1}+\beta _{4}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)
425.2.e.e	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			425.2.e.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
425.2.e.f	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					85.2.e.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

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