Space of modular forms of level 1911, weight 2, and Character 1911.c

• Label: 1911.2.c
• Level: $1911$
• Weight: $2$
• Character orbit: 1911.c
• Rep. character: $\chi_{1911}(883,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $16$
• Sturm bound: $522$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(522\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\), \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1911, [\chi])\).

	Total	New	Old
Modular forms	276	94	182
Cusp forms	244	94	150
Eisenstein series	32	0	32

Trace form

94 * q + 2 * q^3 - 90 * q^4 + 94 * q^9 - 8 * q^10 - 10 * q^12 + 6 * q^13 + 102 * q^16 - 4 * q^17 + 28 * q^22 + 8 * q^23 - 66 * q^25 - 8 * q^26 + 2 * q^27 - 4 * q^29 - 90 * q^36 - 44 * q^38 + 4 * q^39 - 16 * q^40 + 28 * q^43 + 38 * q^48 + 4 * q^51 - 22 * q^52 - 68 * q^53 + 12 * q^61 + 44 * q^62 - 106 * q^64 - 76 * q^65 + 4 * q^66 + 28 * q^68 - 8 * q^69 + 8 * q^74 - 6 * q^75 + 8 * q^78 - 12 * q^79 + 94 * q^81 - 24 * q^82 - 12 * q^87 - 60 * q^88 - 8 * q^90 - 32 * q^92 + 76 * q^94 + 104 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1911, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1911.2.c.a	$1911$	$2$	1911.c	13.b	$2$	$2$	$2$	$15.259$	\(\Q(\sqrt{-1}) \)	None					273.2.c.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-q^{3}-2 q^{4}-3 i q^{5}-2 i q^{6}+\cdots\)
1911.2.c.b	$1911$	$2$	1911.c	13.b	$2$	$2$	$2$	$15.259$	\(\Q(\sqrt{-3}) \)	None					273.2.bj.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-q^{3}-q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)
1911.2.c.c	$1911$	$2$	1911.c	13.b	$2$	$2$	$2$	$15.259$	\(\Q(\sqrt{-1}) \)	None		✓			1911.2.c.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{3}+q^{4}-2 i q^{5}-i q^{6}+\cdots\)
1911.2.c.d	$1911$	$2$	1911.c	13.b	$2$	$2$	$2$	$15.259$	\(\Q(\sqrt{-3}) \)	None					39.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+q^{3}-q^{4}-\beta q^{6}-\beta q^{8}+\cdots\)
1911.2.c.e	$1911$	$2$	1911.c	13.b	$2$	$2$	$2$	$15.259$	\(\Q(\sqrt{-3}) \)	None					273.2.bj.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+q^{3}-q^{4}+2\beta q^{5}-\beta q^{6}+\cdots\)
1911.2.c.f	$1911$	$2$	1911.c	13.b	$2$	$2$	$2$	$15.259$	\(\Q(\sqrt{-1}) \)	None		✓			1911.2.c.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}+q^{4}+2 i q^{5}+i q^{6}+\cdots\)
1911.2.c.g	$1911$	$2$	1911.c	13.b	$2$	$6$	$6$	$15.259$	6.0.1531626496.1	None		✓			1911.2.c.g	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1911.2.c.h	$1911$	$2$	1911.c	13.b	$2$	$6$	$6$	$15.259$	6.0.350464.1	None					273.2.c.b	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1911.2.c.i	$1911$	$2$	1911.c	13.b	$2$	$6$	$6$	$15.259$	6.0.1531626496.1	None		✓			1911.2.c.g	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
1911.2.c.j	$1911$	$2$	1911.c	13.b	$2$	$8$	$8$	$15.259$	8.0.\(\cdots\).1	None					273.2.bj.d	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{3}+(-1-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1911.2.c.k	$1911$	$2$	1911.c	13.b	$2$	$8$	$8$	$15.259$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					273.2.bj.c	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
1911.2.c.l	$1911$	$2$	1911.c	13.b	$2$	$8$	$8$	$15.259$	8.0.\(\cdots\).1	None					273.2.c.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
1911.2.c.m	$1911$	$2$	1911.c	13.b	$2$	$8$	$8$	$15.259$	8.0.\(\cdots\).1	None					273.2.bj.d	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+q^{3}+(-1-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1911.2.c.n	$1911$	$2$	1911.c	13.b	$2$	$8$	$8$	$15.259$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					273.2.bj.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
1911.2.c.o	$1911$	$2$	1911.c	13.b	$2$	$12$	$12$	$15.259$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1911.2.c.o	$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
1911.2.c.p	$1911$	$2$	1911.c	13.b	$2$	$12$	$12$	$15.259$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1911.2.c.o	$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)