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

• Label: 1260.2.bv
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.bv
• Rep. character: $\chi_{1260}(169,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.bv (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	600	72	528
Cusp forms	552	72	480
Eisenstein series	48	0	48

Trace form

72 * q - 2 * q^5 - 8 * q^9 - 6 * q^11 + 8 * q^15 - 2 * q^21 + 6 * q^25 + 28 * q^29 - 12 * q^31 + 26 * q^39 + 8 * q^41 + 42 * q^45 + 36 * q^49 - 10 * q^51 - 12 * q^55 + 44 * q^59 - 12 * q^65 - 4 * q^69 - 32 * q^71 - 24 * q^75 - 6 * q^79 - 40 * q^81 + 24 * q^85 - 80 * q^89 - 12 * q^91 - 36 * q^95 - 108 * q^99

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.bv.a	$1260$	$2$	1260.bv	45.j	$6$	$4$	$2$	$10.061$	\(\Q(\zeta_{12})\)	None		✓			1260.2.bv.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1260.2.bv.b	$1260$	$2$	1260.bv	45.j	$6$	$68$	$34$	$10.061$		None		✓	✓		1260.2.bv.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)