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

• Label: 1260.2.dx
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.dx
• Rep. character: $\chi_{1260}(143,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $384$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.dx (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 420 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	1216	384	832
Cusp forms	1088	384	704
Eisenstein series	128	0	128

Trace form

\( 384 q + 64 q^{28} + 120 q^{40} + 80 q^{58} + 8 q^{70} + 120 q^{82} - 48 q^{88}+O(q^{100}) \)

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

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)