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Properties

Label 2960.2.ba
Level $2960$
Weight $2$
Character orbit 2960.ba
Rep. character $\chi_{2960}(2147,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $864$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.ba (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2960, [\chi])\).

Total New Old
Modular forms 920 864 56
Cusp forms 904 864 40
Eisenstein series 16 0 16

Trace form

\( 864 q + 8 q^{4} + 12 q^{8} - 864 q^{9} + O(q^{10}) \) \( 864 q + 8 q^{4} + 12 q^{8} - 864 q^{9} - 16 q^{12} + 8 q^{16} - 16 q^{19} - 12 q^{20} + 4 q^{22} + 28 q^{28} - 40 q^{30} + 20 q^{32} + 48 q^{34} - 24 q^{35} - 32 q^{36} - 12 q^{38} - 20 q^{40} - 40 q^{42} + 64 q^{43} - 32 q^{46} + 48 q^{47} - 68 q^{48} - 20 q^{50} - 16 q^{51} + 20 q^{52} - 16 q^{58} + 32 q^{59} + 92 q^{60} - 32 q^{61} - 4 q^{62} + 32 q^{64} - 48 q^{67} - 52 q^{68} - 32 q^{69} + 112 q^{70} - 64 q^{71} + 40 q^{72} - 32 q^{75} - 32 q^{76} + 128 q^{78} + 24 q^{80} + 864 q^{81} + 116 q^{82} + 72 q^{84} + 16 q^{86} + 64 q^{88} + 136 q^{90} - 32 q^{91} - 24 q^{92} - 8 q^{94} + 80 q^{95} + 72 q^{96} - 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)