Space of modular forms of level 1260, weight 2, and Character 1260.c

• Label: 1260.2.c
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.c
• Rep. character: $\chi_{1260}(811,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

	Total	New	Old
Modular forms	304	80	224
Cusp forms	272	80	192
Eisenstein series	32	0	32

Trace form

\( 80 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1260.2.c.a	$1260$	$2$	1260.c	28.d	$2$	$4$	$4$	$10.061$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{4}+\cdots\)
1260.2.c.b	$1260$	$2$	1260.c	28.d	$2$	$4$	$4$	$10.061$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{4}+\cdots\)
1260.2.c.c	$1260$	$2$	1260.c	28.d	$2$	$8$	$8$	$10.061$	8.0.342102016.5	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\beta _{2}q^{5}+\cdots\)
1260.2.c.d	$1260$	$2$	1260.c	28.d	$2$	$16$	$16$	$10.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{8}q^{4}+\beta _{3}q^{5}+(-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)
1260.2.c.e	$1260$	$2$	1260.c	28.d	$2$	$16$	$16$	$10.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{8}q^{4}-\beta _{3}q^{5}-\beta _{15}q^{7}+\cdots\)
1260.2.c.f	$1260$	$2$	1260.c	28.d	$2$	$32$	$32$	$10.061$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \)