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Properties

Label 2288.2.dh
Level $2288$
Weight $2$
Character orbit 2288.dh
Rep. character $\chi_{2288}(133,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1120$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2288 = 2^{4} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2288.dh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2288, [\chi])\).

Total New Old
Modular forms 1360 1120 240
Cusp forms 1328 1120 208
Eisenstein series 32 0 32

Trace form

\( 1120 q - 12 q^{6} + O(q^{10}) \) \( 1120 q - 12 q^{6} + 24 q^{12} - 16 q^{14} + 8 q^{20} - 48 q^{27} + 20 q^{28} + 12 q^{36} - 40 q^{38} + 80 q^{40} - 60 q^{42} + 16 q^{44} - 20 q^{46} + 72 q^{48} + 560 q^{49} - 104 q^{50} + 36 q^{52} - 20 q^{56} - 72 q^{58} + 64 q^{59} - 48 q^{60} - 48 q^{62} + 72 q^{64} + 16 q^{65} - 40 q^{66} + 16 q^{68} + 40 q^{70} + 148 q^{72} - 56 q^{74} - 64 q^{76} + 164 q^{78} + 560 q^{81} - 116 q^{82} - 152 q^{84} - 96 q^{86} - 352 q^{90} - 32 q^{91} + 96 q^{92} + 96 q^{93} - 32 q^{94} - 368 q^{96} - 36 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2288, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2288, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)