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

• Label: 1260.2.bm
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.bm
• Rep. character: $\chi_{1260}(109,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	624	40	584
Cusp forms	528	40	488
Eisenstein series	96	0	96

Trace form

\( 40 q - q^{5} + O(q^{10}) \)

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.bm.a	$1260$	$2$	1260.bm	35.j	$6$	$4$	$2$	$10.061$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
1260.2.bm.b	$1260$	$2$	1260.bm	35.j	$6$	$4$	$2$	$10.061$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+(2-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
1260.2.bm.c	$1260$	$2$	1260.bm	35.j	$6$	$16$	$8$	$10.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{8}-\beta _{12}-\beta _{14})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1260.2.bm.d	$1260$	$2$	1260.bm	35.j	$6$	$16$	$8$	$10.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{5}+(\beta _{5}-\beta _{6}+\beta _{14})q^{7}-\beta _{15}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)