Space of modular forms of level 925, weight 2, and Character 925.b

• Label: 925.2.b
• Level: $925$
• Weight: $2$
• Character orbit: 925.b
• Rep. character: $\chi_{925}(149,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $9$
• Sturm bound: $190$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(190\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).

	Total	New	Old
Modular forms	102	54	48
Cusp forms	90	54	36
Eisenstein series	12	0	12

Trace form

54 * q - 46 * q^4 - 12 * q^6 - 38 * q^9 - 4 * q^11 + 4 * q^14 + 30 * q^16 - 28 * q^21 + 36 * q^24 + 4 * q^26 + 12 * q^29 + 4 * q^31 + 40 * q^34 + 6 * q^36 - 12 * q^39 - 8 * q^41 + 32 * q^44 - 64 * q^46 - 74 * q^49 - 8 * q^51 - 40 * q^54 + 12 * q^56 + 4 * q^59 - 48 * q^61 + 14 * q^64 + 104 * q^66 + 12 * q^69 - 52 * q^71 - 10 * q^74 + 60 * q^76 - 28 * q^79 - 10 * q^81 + 44 * q^84 + 20 * q^86 + 24 * q^89 - 112 * q^94 - 116 * q^96 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(925, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
925.2.b.a	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	\(\Q(\sqrt{-1}) \)	None					185.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}+5 i q^{7}+\cdots\)
925.2.b.b	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	\(\Q(\sqrt{-1}) \)	None					37.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-3 i q^{3}-2 q^{4}+6 q^{6}+\cdots\)
925.2.b.c	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	\(\Q(\sqrt{-1}) \)	None					185.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}+q^{4}-2 q^{6}-2 i q^{7}+\cdots\)
925.2.b.d	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	\(\Q(\sqrt{-1}) \)	None					185.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}+3 i q^{7}+2 q^{9}-5 q^{11}+\cdots\)
925.2.b.e	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	\(\Q(\sqrt{-1}) \)	None					37.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}-i q^{7}+2 q^{9}+3 q^{11}+\cdots\)
925.2.b.f	$925$	$2$	925.b	5.b	$2$	$10$	$10$	$7.386$	10.0.\(\cdots\).1	None					185.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{8})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
925.2.b.g	$925$	$2$	925.b	5.b	$2$	$10$	$10$	$7.386$	10.0.\(\cdots\).1	None					185.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}-\beta _{7}q^{3}+(-2+\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots\)
925.2.b.h	$925$	$2$	925.b	5.b	$2$	$10$	$10$	$7.386$	10.0.\(\cdots\).1	None		✓			925.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
925.2.b.i	$925$	$2$	925.b	5.b	$2$	$14$	$14$	$7.386$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓		925.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(925, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)