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Properties

Label 1320.2.cc
Level $1320$
Weight $2$
Character orbit 1320.cc
Rep. character $\chi_{1320}(211,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $384$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1320.cc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1184 384 800
Cusp forms 1120 384 736
Eisenstein series 64 0 64

Trace form

\( 384 q + 8 q^{4} - 96 q^{9} + O(q^{10}) \) \( 384 q + 8 q^{4} - 96 q^{9} - 16 q^{11} + 20 q^{14} + 20 q^{18} - 8 q^{20} + 48 q^{22} - 60 q^{24} + 96 q^{25} - 8 q^{26} - 20 q^{28} + 48 q^{34} + 8 q^{36} + 60 q^{38} + 24 q^{42} - 8 q^{44} + 20 q^{46} - 32 q^{48} - 96 q^{49} + 100 q^{52} + 24 q^{56} - 44 q^{58} + 32 q^{59} + 68 q^{64} + 28 q^{66} - 32 q^{67} - 44 q^{70} - 20 q^{72} - 100 q^{74} - 64 q^{78} - 96 q^{81} - 12 q^{82} - 120 q^{84} - 112 q^{86} + 20 q^{88} + 112 q^{91} - 104 q^{92} - 120 q^{94} - 100 q^{96} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)