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

• Label: 925.2.f
• Level: $925$
• Weight: $2$
• Character orbit: 925.f
• Rep. character: $\chi_{925}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $110$
• Newform subspaces: $6$
• Sturm bound: $190$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(190\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	202	118	84
Cusp forms	178	110	68
Eisenstein series	24	8	16

Trace form

110 * q - 4 * q^3 - 106 * q^4 - 4 * q^6 + 4 * q^7 + 32 * q^12 + 90 * q^16 + 20 * q^17 + 22 * q^18 + 12 * q^19 - 20 * q^22 - 12 * q^24 - 24 * q^26 + 20 * q^27 + 8 * q^28 + 2 * q^29 + 8 * q^31 - 8 * q^33 + 12 * q^37 + 60 * q^38 + 48 * q^39 - 64 * q^42 + 16 * q^46 - 12 * q^47 - 60 * q^48 - 4 * q^51 + 10 * q^53 - 92 * q^54 - 64 * q^56 + 22 * q^58 + 16 * q^59 + 18 * q^61 + 32 * q^62 - 36 * q^63 + 30 * q^64 + 28 * q^66 - 8 * q^67 - 8 * q^68 + 56 * q^69 - 40 * q^71 - 70 * q^72 - 30 * q^73 - 14 * q^74 - 140 * q^76 + 36 * q^77 + 36 * q^78 - 190 * q^81 + 4 * q^82 + 24 * q^83 - 80 * q^86 + 64 * q^87 + 24 * q^88 - 22 * q^89 - 16 * q^91 - 80 * q^94 + 44 * q^96 - 56 * q^97 + 102 * q^98 + 128 * 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.f.a	$925$	$2$	925.f	185.f	$4$	$2$	$1$	$7.386$	\(\Q(\sqrt{-1}) \)	None					185.2.f.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+i q^{2}+(-2 i-2)q^{3}+q^{4}+(-2 i+2)q^{6}+\cdots\)
925.2.f.b	$925$	$2$	925.f	185.f	$4$	$2$	$1$	$7.386$	\(\Q(\sqrt{-1}) \)	None					185.2.f.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+i q^{2}+(i+1)q^{3}+q^{4}+(i-1)q^{6}+\cdots\)
925.2.f.c	$925$	$2$	925.f	185.f	$4$	$6$	$3$	$7.386$	6.0.350464.1	None					185.2.f.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
925.2.f.d	$925$	$2$	925.f	185.f	$4$	$24$	$12$	$7.386$		None					185.2.f.d	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{4}]$
925.2.f.e	$925$	$2$	925.f	185.f	$4$	$28$	$14$	$7.386$		None		✓			925.2.f.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
925.2.f.f	$925$	$2$	925.f	185.f	$4$	$48$	$24$	$7.386$		None		✓	✓		925.2.f.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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