Space of modular forms of level 1305, weight 2, and Character 1305.d

• Label: 1305.2.d
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.d
• Rep. character: $\chi_{1305}(811,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $6$
• Sturm bound: $360$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(360\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

	Total	New	Old
Modular forms	188	50	138
Cusp forms	172	50	122
Eisenstein series	16	0	16

Trace form

50 * q - 46 * q^4 - 2 * q^5 - 4 * q^7 + 4 * q^13 + 46 * q^16 + 6 * q^20 + 24 * q^22 + 28 * q^23 + 50 * q^25 - 4 * q^28 - 10 * q^29 + 4 * q^34 - 12 * q^35 + 8 * q^38 + 10 * q^49 - 92 * q^52 + 36 * q^53 + 8 * q^58 + 16 * q^59 - 8 * q^62 + 34 * q^64 + 12 * q^65 - 36 * q^67 + 80 * q^71 + 12 * q^74 + 2 * q^80 - 40 * q^82 - 44 * q^83 + 80 * q^86 - 40 * q^88 + 32 * q^91 - 132 * q^92 - 24 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1305.2.d.a	$1305$	$2$	1305.d	29.b	$2$	$4$	$4$	$10.420$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					145.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
1305.2.d.b	$1305$	$2$	1305.d	29.b	$2$	$6$	$6$	$10.420$	6.0.16516096.1	None					145.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots\)
1305.2.d.c	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	10.0.\(\cdots\).1	None					435.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
1305.2.d.d	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	10.0.\(\cdots\).1	None					435.2.d.a	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}-\beta _{5}q^{7}+\cdots\)
1305.2.d.e	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1305.2.d.e	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+\beta _{7}q^{7}+\cdots\)
1305.2.d.f	$1305$	$2$	1305.d	29.b	$2$	$10$	$10$	$10.420$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1305.2.d.e	$2$	$0$	\(0\)	\(0\)	\(10\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)