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

• Label: 425.2.b
• Level: $425$
• Weight: $2$
• Character orbit: 425.b
• Rep. character: $\chi_{425}(324,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $90$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(90\)
Trace bound:			\(6\)
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	52	24	28
Cusp forms	40	24	16
Eisenstein series	12	0	12

Trace form

24 * q - 24 * q^4 - 4 * q^6 - 20 * q^9 - 4 * q^14 + 40 * q^16 - 28 * q^21 + 16 * q^24 - 20 * q^26 + 4 * q^29 + 36 * q^31 - 4 * q^34 + 4 * q^36 - 56 * q^39 - 4 * q^41 + 24 * q^44 + 28 * q^46 - 4 * q^49 + 8 * q^51 + 80 * q^54 - 8 * q^56 - 8 * q^59 - 16 * q^61 - 104 * q^64 - 96 * q^66 + 56 * q^71 + 68 * q^74 + 32 * q^76 - 68 * q^79 + 24 * q^81 + 140 * q^84 - 64 * q^86 + 56 * q^89 + 64 * q^94 - 156 * q^96 - 12 * 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.b.a	$425$	$2$	425.b	5.b	$2$	$2$	$2$	$3.394$	\(\Q(\sqrt{-1}) \)	None		✓			425.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}+i q^{7}+\cdots\)
425.2.b.b	$425$	$2$	425.b	5.b	$2$	$2$	$2$	$3.394$	\(\Q(\sqrt{-1}) \)	None					17.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-4 i q^{7}+3 i q^{8}+3 q^{9}+\cdots\)
425.2.b.c	$425$	$2$	425.b	5.b	$2$	$2$	$2$	$3.394$	\(\Q(\sqrt{-1}) \)	None					85.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}+q^{4}+2 q^{6}-2 i q^{7}+\cdots\)
425.2.b.d	$425$	$2$	425.b	5.b	$2$	$4$	$4$	$3.394$	\(\Q(\zeta_{12})\)	None					85.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{2}+(-\beta_{2}-\beta_1)q^{3}-q^{4}+\cdots\)
425.2.b.e	$425$	$2$	425.b	5.b	$2$	$4$	$4$	$3.394$	\(\Q(\zeta_{8})\)	None					85.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+(\beta_{2}-2\beta_1)q^{3}+\cdots\)
425.2.b.f	$425$	$2$	425.b	5.b	$2$	$10$	$10$	$3.394$	10.0.\(\cdots\).1	None		✓	✓		425.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}+\beta _{6}q^{3}+(-2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)

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

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