Space of modular forms of level 455, weight 2, and trivial character

• Label: 455.2.a
• Level: $455$
• Weight: $2$
• Character orbit: 455.a
• Rep. character: $\chi_{455}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $6$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(455))\).

	Total	New	Old
Modular forms	60	23	37
Cusp forms	53	23	30
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(3\)	\(1\)	\(2\)		\(3\)	\(1\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(10\)	\(4\)	\(6\)		\(9\)	\(4\)	\(5\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(12\)	\(7\)	\(5\)		\(11\)	\(7\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(10\)	\(4\)	\(6\)		\(9\)	\(4\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(8\)	\(6\)	\(2\)		\(7\)	\(6\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(20\)	\(2\)	\(18\)		\(17\)	\(2\)	\(15\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(40\)	\(21\)	\(19\)		\(36\)	\(21\)	\(15\)		\(4\)	\(0\)	\(4\)

Trace form

23 * q + 5 * q^2 + 4 * q^3 + 29 * q^4 - q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 35 * q^9 + 5 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + q^14 + 4 * q^15 + 45 * q^16 + 14 * q^17 + q^18 + 28 * q^19 - 7 * q^20 - 4 * q^21 + 12 * q^22 - 8 * q^23 - 12 * q^24 + 23 * q^25 - 3 * q^26 - 8 * q^27 + 21 * q^28 - 6 * q^29 - 12 * q^30 - 7 * q^32 + 48 * q^33 + 10 * q^34 - q^35 + 41 * q^36 + 10 * q^37 - 36 * q^38 - 4 * q^39 + 33 * q^40 + 38 * q^41 - 12 * q^42 + 12 * q^43 - 36 * q^44 - 13 * q^45 + 8 * q^46 - 32 * q^47 - 68 * q^48 + 23 * q^49 + 5 * q^50 - 8 * q^51 - 7 * q^52 + 2 * q^53 - 56 * q^54 - 12 * q^55 - 3 * q^56 + 32 * q^57 - 26 * q^58 - 28 * q^59 - 4 * q^60 + 26 * q^61 - 40 * q^62 + 23 * q^63 + 61 * q^64 + 7 * q^65 - 80 * q^66 + 44 * q^67 - 14 * q^68 - 32 * q^69 + q^70 - 75 * q^72 + 86 * q^73 - 42 * q^74 + 4 * q^75 + 36 * q^76 + 4 * q^77 - 4 * q^78 + 16 * q^79 - 31 * q^80 + 95 * q^81 - 30 * q^82 + 12 * q^83 - 28 * q^84 + 22 * q^85 - 76 * q^86 - 40 * q^87 - 36 * q^88 - 42 * q^89 + 9 * q^90 - q^91 - 88 * q^92 - 32 * q^93 - 48 * q^94 - 12 * q^95 - 140 * q^96 + 30 * q^97 + 5 * q^98 - 76 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(455))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	7	13
455.2.a.a	$455$	$2$	455.a	1.a	$1$	$1$	$1$	$3.633$	\(\Q\)	None	✓	✓	✓	✓	455.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
455.2.a.b	$455$	$2$	455.a	1.a	$1$	$1$	$1$	$3.633$	\(\Q\)	None	✓	✓	✓	✓	455.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-3q^{9}+\cdots\)
455.2.a.c	$455$	$2$	455.a	1.a	$1$	$4$	$4$	$3.633$	4.4.12197.1	None	✓	✓	✓	✓	455.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
455.2.a.d	$455$	$2$	455.a	1.a	$1$	$4$	$4$	$3.633$	4.4.1957.1	None	✓	✓	✓	✓	455.2.a.d	$1$	$0$	\(3\)	\(4\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+\cdots\)
455.2.a.e	$455$	$2$	455.a	1.a	$1$	$6$	$6$	$3.633$	6.6.45853772.1	None	✓	✓	✓	✓	455.2.a.e	$1$	$0$	\(3\)	\(0\)	\(6\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
455.2.a.f	$455$	$2$	455.a	1.a	$1$	$7$	$7$	$3.633$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	455.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-7\)	\(7\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(455))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(455)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)