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Properties

Label 2960.2.hi
Level $2960$
Weight $2$
Character orbit 2960.hi
Rep. character $\chi_{2960}(91,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $3648$
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.hi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 592 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(912\)

Dimensions

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

Total New Old
Modular forms 5520 3648 1872
Cusp forms 5424 3648 1776
Eisenstein series 96 0 96

Trace form

\( 3648 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + O(q^{10}) \) \( 3648 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 60 q^{12} - 60 q^{16} + 60 q^{18} - 60 q^{22} + 60 q^{24} - 60 q^{28} - 48 q^{30} - 48 q^{32} + 96 q^{37} - 48 q^{43} - 24 q^{44} + 120 q^{46} - 120 q^{51} - 48 q^{53} + 60 q^{54} + 168 q^{56} + 36 q^{64} - 132 q^{66} - 300 q^{68} + 336 q^{72} + 12 q^{74} - 144 q^{76} - 48 q^{77} + 192 q^{82} + 120 q^{83} - 264 q^{84} + 120 q^{88} + 420 q^{92} - 144 q^{94} - 108 q^{98} - 312 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 2}\)