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

• Label: 1305.2.c
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.c
• Rep. character: $\chi_{1305}(784,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $12$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	188	70	118
Cusp forms	172	70	102
Eisenstein series	16	0	16

Trace form

70 * q - 66 * q^4 + 4 * q^5 - 14 * q^10 + 8 * q^11 - 8 * q^14 + 82 * q^16 + 20 * q^19 - 12 * q^20 - 12 * q^26 - 6 * q^29 - 40 * q^31 - 12 * q^34 + 4 * q^35 + 10 * q^40 + 20 * q^41 - 8 * q^44 + 56 * q^46 - 62 * q^49 + 10 * q^50 + 14 * q^55 + 8 * q^56 + 16 * q^59 - 44 * q^61 - 90 * q^64 + 10 * q^65 - 32 * q^70 - 24 * q^71 + 60 * q^74 - 84 * q^76 + 56 * q^79 + 52 * q^80 + 52 * q^85 - 4 * q^86 - 36 * q^89 + 8 * q^91 + 36 * q^94 + 12 * q^95

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.c.a	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	\(\Q(\sqrt{-1}) \)	None					435.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}+(-i+2)q^{5}-2 i q^{7}+\cdots\)
1305.2.c.b	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	\(\Q(\sqrt{-1}) \)	None					435.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+(-2 i-1)q^{5}+2 i q^{7}+\cdots\)
1305.2.c.c	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	\(\Q(\sqrt{-5}) \)	None		✓			1305.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+\beta q^{5}-2\beta q^{7}-5q^{11}-2\beta q^{13}+\cdots\)
1305.2.c.d	$1305$	$2$	1305.c	5.b	$2$	$2$	$2$	$10.420$	\(\Q(\sqrt{-5}) \)	None		✓			1305.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}-\beta q^{5}-2\beta q^{7}+5q^{11}-2\beta q^{13}+\cdots\)
1305.2.c.e	$1305$	$2$	1305.c	5.b	$2$	$4$	$4$	$10.420$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					145.2.b.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
1305.2.c.f	$1305$	$2$	1305.c	5.b	$2$	$4$	$4$	$10.420$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					145.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
1305.2.c.g	$1305$	$2$	1305.c	5.b	$2$	$4$	$4$	$10.420$	\(\Q(\zeta_{8})\)	None					435.2.c.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+q^{4}+(2\beta_1+1)q^{5}+\beta_{2} q^{7}+\cdots\)
1305.2.c.h	$1305$	$2$	1305.c	5.b	$2$	$6$	$6$	$10.420$	6.0.84345856.2	None					145.2.b.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
1305.2.c.i	$1305$	$2$	1305.c	5.b	$2$	$10$	$10$	$10.420$	10.0.\(\cdots\).1	None					435.2.c.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1305.2.c.j	$1305$	$2$	1305.c	5.b	$2$	$10$	$10$	$10.420$	10.0.\(\cdots\).1	None					435.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1305.2.c.k	$1305$	$2$	1305.c	5.b	$2$	$12$	$12$	$10.420$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1305.2.c.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
1305.2.c.l	$1305$	$2$	1305.c	5.b	$2$	$12$	$12$	$10.420$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1305.2.c.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{7}q^{5}+\beta _{3}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)