Space of modular forms of level 1053, weight 2, and Character 1053.b

• Label: 1053.2.b
• Level: $1053$
• Weight: $2$
• Character orbit: 1053.b
• Rep. character: $\chi_{1053}(649,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $11$
• Sturm bound: $252$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(252\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1053, [\chi])\).

	Total	New	Old
Modular forms	138	60	78
Cusp forms	114	52	62
Eisenstein series	24	8	16

Trace form

52 * q - 44 * q^4 - 28 * q^10 - 6 * q^13 + 36 * q^16 + 20 * q^22 - 20 * q^25 + 52 * q^40 + 20 * q^43 - 20 * q^49 + 26 * q^52 - 28 * q^55 - 12 * q^61 + 12 * q^64 + 24 * q^79 - 28 * q^82 - 92 * q^88 + 12 * q^91 - 40 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1053, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1053.2.b.a	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	\(\Q(\sqrt{-3}) \)	None		✓			1053.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
1053.2.b.b	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	\(\Q(\sqrt{-3}) \)	None		✓			1053.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
1053.2.b.c	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	\(\Q(\sqrt{-3}) \)	None		✓			1053.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-q^{4}+2\beta q^{5}-\beta q^{7}-\beta q^{8}+\cdots\)
1053.2.b.d	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	\(\Q(\sqrt{-3}) \)	None		✓			1053.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-q^{4}+2\beta q^{5}+\beta q^{7}-\beta q^{8}+\cdots\)
1053.2.b.e	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	\(\Q(\sqrt{-3}) \)	None					117.2.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}+\beta q^{5}-\beta q^{7}+\beta q^{11}+(\beta-1)q^{13}+\cdots\)
1053.2.b.f	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	\(\Q(\sqrt{-3}) \)	None					117.2.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}+\beta q^{5}+\beta q^{7}+\beta q^{11}+(-\beta-1)q^{13}+\cdots\)
1053.2.b.g	$1053$	$2$	1053.b	13.b	$2$	$4$	$4$	$8.408$	\(\Q(i, \sqrt{5})\)	None		✓			1053.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.h	$1053$	$2$	1053.b	13.b	$2$	$4$	$4$	$8.408$	\(\Q(i, \sqrt{5})\)	None		✓			1053.2.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.i	$1053$	$2$	1053.b	13.b	$2$	$10$	$10$	$8.408$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					117.2.t.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.j	$1053$	$2$	1053.b	13.b	$2$	$10$	$10$	$8.408$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					117.2.t.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1053.2.b.k	$1053$	$2$	1053.b	13.b	$2$	$12$	$12$	$8.408$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		1053.2.b.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1053, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1053, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)