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

• Label: 925.2.bn
• Level: $925$
• Weight: $2$
• Character orbit: 925.bn
• Rep. character: $\chi_{925}(18,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $660$
• 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.bn (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{36})\)
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	1212	708	504
Cusp forms	1068	660	408
Eisenstein series	144	48	96

Trace form

660 * q + 12 * q^2 + 6 * q^3 - 24 * q^6 + 12 * q^7 + 24 * q^8 - 36 * q^11 - 36 * q^12 + 12 * q^13 + 48 * q^14 - 24 * q^16 + 30 * q^17 + 90 * q^18 - 24 * q^21 + 24 * q^22 + 6 * q^23 + 36 * q^24 - 12 * q^26 + 42 * q^27 - 48 * q^31 - 12 * q^32 + 24 * q^33 + 36 * q^37 - 60 * q^38 - 48 * q^39 + 54 * q^41 + 42 * q^42 + 24 * q^43 - 24 * q^46 + 6 * q^47 + 6 * q^48 - 72 * q^49 - 24 * q^51 - 60 * q^52 + 90 * q^53 - 24 * q^56 + 36 * q^57 - 12 * q^61 + 96 * q^62 + 6 * q^63 - 246 * q^64 - 528 * q^66 - 30 * q^67 + 204 * q^69 - 120 * q^71 - 216 * q^72 - 90 * q^73 + 222 * q^74 - 144 * q^76 - 24 * q^77 + 138 * q^78 - 48 * q^79 - 156 * q^81 + 18 * q^82 + 72 * q^83 + 96 * q^86 + 114 * q^87 - 198 * q^88 + 24 * q^89 - 120 * q^91 + 54 * q^92 - 42 * q^93 - 144 * q^94 - 192 * q^96 - 54 * q^97 + 60 * q^98 - 384 * 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.bn.a	$925$	$2$	925.bn	185.z	$36$	$144$	$12$	$7.386$		None		✓			925.2.bn.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
925.2.bn.b	$925$	$2$	925.bn	185.z	$36$	$204$	$17$	$7.386$		None					185.2.z.a	$2$	$0$	\(12\)	\(6\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{36}]$
925.2.bn.c	$925$	$2$	925.bn	185.z	$36$	$312$	$26$	$7.386$		None		✓	✓		925.2.bn.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

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

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