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

• Label: 425.2.j
• Level: $425$
• Weight: $2$
• Character orbit: 425.j
• Rep. character: $\chi_{425}(149,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $90$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(90\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	104	56	48
Cusp forms	80	48	32
Eisenstein series	24	8	16

Trace form

48 * q + 48 * q^4 + 12 * q^6 - 16 * q^11 - 20 * q^14 + 16 * q^16 - 16 * q^21 + 8 * q^24 + 36 * q^29 - 12 * q^31 - 36 * q^34 + 8 * q^39 - 36 * q^41 - 80 * q^44 + 12 * q^46 - 16 * q^51 - 88 * q^54 - 32 * q^56 + 64 * q^61 + 32 * q^64 + 144 * q^69 + 16 * q^71 - 4 * q^74 + 44 * q^79 + 40 * q^81 - 72 * q^84 - 24 * q^86 - 48 * q^91 - 20 * q^96 - 60 * 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.j.a	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			425.2.e.c	$2$	$0$	\(-4\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{8}q^{2}-\beta _{4}q^{3}+(1-\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{6}+\cdots\)
425.2.j.b	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					85.2.e.a	$2$	$0$	\(-4\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(1+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
425.2.j.c	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					85.2.e.a	$2$	$0$	\(4\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(1+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
425.2.j.d	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			425.2.e.c	$2$	$0$	\(4\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}-\beta _{3}q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{6}+\cdots)q^{6}+\cdots\)

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

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