Space of modular forms of level 1320, weight 2, and Character 1320.p

• Label: 1320.2.p
• Level: $1320$
• Weight: $2$
• Character orbit: 1320.p
• Rep. character: $\chi_{1320}(461,\cdot)$
• Character field: $\Q$
• Dimension: $192$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

	Total	New	Old
Modular forms	296	192	104
Cusp forms	280	192	88
Eisenstein series	16	0	16

Trace form

\( 192 q - 32 q^{16} - 28 q^{22} + 192 q^{25} + 8 q^{33} + 24 q^{34} + 36 q^{36} + 64 q^{42} + 64 q^{48} - 192 q^{49} - 64 q^{58} + 28 q^{60} - 20 q^{66} - 24 q^{70} + 32 q^{78} + 16 q^{81} + 8 q^{82} - 36 q^{88}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)