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

• Label: 1260.2.dq
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.dq
• Rep. character: $\chi_{1260}(73,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $80$
• Newform subspaces: $3$
• 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.dq (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	1248	80	1168
Cusp forms	1056	80	976
Eisenstein series	192	0	192

Trace form

80 * q + 6 * q^5 - 6 * q^7 - 8 * q^11 - 18 * q^17 - 10 * q^25 - 12 * q^31 + 20 * q^35 + 2 * q^37 + 12 * q^43 - 6 * q^47 - 30 * q^53 + 12 * q^61 + 18 * q^65 - 24 * q^67 + 24 * q^71 - 42 * q^73 + 74 * q^77 + 16 * q^85 + 64 * q^91 + 34 * q^95

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1260.2.dq.a	$1260$	$2$	1260.dq	35.k	$12$	$16$	$4$	$10.061$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					140.2.u.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2\beta _{1}-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{10}+\beta _{11}+\cdots)q^{5}+\cdots\)
1260.2.dq.b	$1260$	$2$	1260.dq	35.k	$12$	$32$	$8$	$10.061$		None		✓			1260.2.dq.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$
1260.2.dq.c	$1260$	$2$	1260.dq	35.k	$12$	$32$	$8$	$10.061$		None					420.2.bo.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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