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

• Label: 925.2.y
• Level: $925$
• Weight: $2$
• Character orbit: 925.y
• Rep. character: $\chi_{925}(193,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $220$
• Newform subspaces: $3$
• Sturm bound: $190$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(190\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	404	236	168
Cusp forms	356	220	136
Eisenstein series	48	16	32

Trace form

220 * q + 6 * q^2 + 4 * q^3 + 106 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 24 * q^14 - 102 * q^16 + 10 * q^17 + 8 * q^18 - 12 * q^19 - 12 * q^21 + 14 * q^22 + 48 * q^24 - 68 * q^27 - 14 * q^28 - 2 * q^29 + 4 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 + 48 * q^39 - 90 * q^41 + 40 * q^42 + 108 * q^44 - 28 * q^46 + 24 * q^47 - 60 * q^48 - 72 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 + 92 * q^54 + 52 * q^56 - 90 * q^57 - 16 * q^58 - 16 * q^59 + 48 * q^61 + 22 * q^62 + 48 * q^63 - 276 * q^64 - 40 * q^66 + 56 * q^67 + 20 * q^68 - 32 * q^69 - 20 * q^71 - 32 * q^72 - 60 * q^73 - 52 * q^74 - 40 * q^76 - 6 * q^77 + 24 * q^78 - 48 * q^79 + 22 * q^81 + 8 * q^82 - 12 * q^83 + 56 * q^86 + 32 * q^87 + 36 * q^88 + 46 * q^89 + 28 * q^91 - 156 * q^92 + 30 * q^93 - 64 * q^94 + 112 * q^96 - 16 * q^97 - 48 * q^98 + 64 * 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.y.a	$925$	$2$	925.y	185.u	$12$	$56$	$14$	$7.386$		None		✓			925.2.t.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
925.2.y.b	$925$	$2$	925.y	185.u	$12$	$68$	$17$	$7.386$		None					185.2.p.a	$2$	$0$	\(6\)	\(4\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$
925.2.y.c	$925$	$2$	925.y	185.u	$12$	$96$	$24$	$7.386$		None		✓	✓		925.2.t.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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