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

• Label: 1260.2.ba
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.ba
• Rep. character: $\chi_{1260}(433,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $576$
• Trace bound: $7$

Defining parameters

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

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

\( 40 q + 6 q^{7} + O(q^{10}) \)

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.ba.a	$1260$	$2$	1260.ba	35.f	$4$	$8$	$4$	$10.061$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{2}-\beta _{6})q^{5}+(\beta _{4}-\beta _{7})q^{7}+(1-\beta _{4}+\cdots)q^{11}+\cdots\)
1260.2.ba.b	$1260$	$2$	1260.ba	35.f	$4$	$16$	$8$	$10.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{7}+\beta _{11}+\beta _{13})q^{5}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
1260.2.ba.c	$1260$	$2$	1260.ba	35.f	$4$	$16$	$8$	$10.061$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{16}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{5}+(1+\beta _{1}-\beta _{4})q^{7}-\beta _{2}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)