Space of modular forms of level 455, weight 2, and Character 455.c

• Label: 455.2.c
• Level: $455$
• Weight: $2$
• Character orbit: 455.c
• Rep. character: $\chi_{455}(274,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(455, [\chi])\).

	Total	New	Old
Modular forms	60	36	24
Cusp forms	52	36	16
Eisenstein series	8	0	8

Trace form

36 * q - 28 * q^4 + 4 * q^5 - 8 * q^6 - 44 * q^9 - 8 * q^10 + 16 * q^11 - 12 * q^15 + 28 * q^16 + 16 * q^19 + 12 * q^20 + 8 * q^21 - 32 * q^24 - 18 * q^25 - 4 * q^29 - 8 * q^30 + 8 * q^31 + 40 * q^34 + 2 * q^35 + 76 * q^36 - 16 * q^39 + 36 * q^40 - 72 * q^44 + 32 * q^45 - 32 * q^46 - 36 * q^49 - 8 * q^50 - 64 * q^51 + 80 * q^54 - 28 * q^55 - 24 * q^56 + 40 * q^59 - 28 * q^60 + 36 * q^64 + 2 * q^65 + 72 * q^66 + 8 * q^69 - 8 * q^70 + 40 * q^71 - 8 * q^74 - 52 * q^75 - 72 * q^76 - 12 * q^79 - 88 * q^80 + 4 * q^81 - 24 * q^84 + 28 * q^85 + 64 * q^86 + 32 * q^89 - 116 * q^90 + 8 * q^91 - 8 * q^94 - 46 * q^95 + 128 * q^96 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(455, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
455.2.c.a	$455$	$2$	455.c	5.b	$2$	$2$	$2$	$3.633$	\(\Q(\sqrt{-1}) \)	None		✓			455.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}+q^{4}+(i-2)q^{5}+\cdots\)
455.2.c.b	$455$	$2$	455.c	5.b	$2$	$14$	$14$	$3.633$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			455.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
455.2.c.c	$455$	$2$	455.c	5.b	$2$	$20$	$20$	$3.633$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		455.2.c.c	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{19}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(455, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(455, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)