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

• Label: 455.2.j
• Level: $455$
• Weight: $2$
• Character orbit: 455.j
• Rep. character: $\chi_{455}(261,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	120	64	56
Cusp forms	104	64	40
Eisenstein series	16	0	16

Trace form

64 * q + 4 * q^2 - 28 * q^4 + 4 * q^5 + 8 * q^6 - 24 * q^8 - 36 * q^9 + 8 * q^11 - 20 * q^12 - 8 * q^13 + 16 * q^14 - 4 * q^16 - 4 * q^17 - 24 * q^20 - 20 * q^21 - 40 * q^22 - 4 * q^23 + 28 * q^24 - 32 * q^25 + 24 * q^27 + 8 * q^29 - 4 * q^30 - 4 * q^31 + 8 * q^32 + 40 * q^33 + 32 * q^34 + 4 * q^35 + 88 * q^36 - 24 * q^38 + 16 * q^41 - 80 * q^42 - 16 * q^43 - 20 * q^44 + 12 * q^46 + 32 * q^47 + 88 * q^48 - 12 * q^49 - 8 * q^50 - 40 * q^51 + 12 * q^52 + 12 * q^53 + 36 * q^54 + 8 * q^55 - 64 * q^56 + 8 * q^57 - 20 * q^58 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 128 * q^62 - 84 * q^63 - 8 * q^64 + 12 * q^66 + 32 * q^67 + 24 * q^68 - 80 * q^69 + 36 * q^70 - 56 * q^71 - 24 * q^72 + 16 * q^73 - 28 * q^74 - 40 * q^76 + 12 * q^77 + 40 * q^78 + 32 * q^79 + 28 * q^80 - 56 * q^81 - 32 * q^82 + 8 * q^83 + 120 * q^84 + 8 * q^85 + 40 * q^86 - 68 * q^87 + 68 * q^88 - 28 * q^89 - 8 * q^91 - 24 * q^92 + 4 * q^93 + 92 * q^94 + 8 * q^95 - 44 * q^96 + 24 * q^97 - 44 * q^98 - 40 * 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.j.a	$455$	$2$	455.j	7.c	$3$	$2$	$1$	$3.633$	\(\Q(\sqrt{-3}) \)	None		✓			455.2.j.a	$2$	$1$	\(-1\)	\(-3\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
455.2.j.b	$455$	$2$	455.j	7.c	$3$	$2$	$1$	$3.633$	\(\Q(\sqrt{-3}) \)	None		✓			455.2.j.b	$2$	$0$	\(1\)	\(-2\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
455.2.j.c	$455$	$2$	455.j	7.c	$3$	$2$	$1$	$3.633$	\(\Q(\sqrt{-3}) \)	None		✓			455.2.j.c	$2$	$0$	\(1\)	\(3\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
455.2.j.d	$455$	$2$	455.j	7.c	$3$	$8$	$4$	$3.633$	8.0.42575625.1	None		✓			455.2.j.d	$2$	$0$	\(-1\)	\(3\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\beta _{7})q^{2}+\cdots\)
455.2.j.e	$455$	$2$	455.j	7.c	$3$	$14$	$7$	$3.633$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			455.2.j.e	$2$	$0$	\(2\)	\(-1\)	\(-7\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{2}-\beta _{10}q^{3}+(\beta _{5}-\beta _{10})q^{4}+\cdots\)
455.2.j.f	$455$	$2$	455.j	7.c	$3$	$16$	$8$	$3.633$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			455.2.j.f	$2$	$0$	\(1\)	\(-4\)	\(8\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{2}+(-\beta _{4}+\beta _{5})q^{3}+(-\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots\)
455.2.j.g	$455$	$2$	455.j	7.c	$3$	$20$	$10$	$3.633$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		455.2.j.g	$2$	$0$	\(1\)	\(4\)	\(10\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{12}q^{3}+(-1-\beta _{9}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(455, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)