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Properties

Label 2156.2.bn
Level $2156$
Weight $2$
Character orbit 2156.bn
Rep. character $\chi_{2156}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1856$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2156.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2156, [\chi])\).

Total New Old
Modular forms 2816 1984 832
Cusp forms 2560 1856 704
Eisenstein series 256 128 128

Trace form

\( 1856 q - q^{2} + 7 q^{4} + 18 q^{5} - 16 q^{8} + 222 q^{9} + O(q^{10}) \) \( 1856 q - q^{2} + 7 q^{4} + 18 q^{5} - 16 q^{8} + 222 q^{9} + 24 q^{10} + 24 q^{12} + 27 q^{16} + 18 q^{17} + 11 q^{18} - 100 q^{22} + 81 q^{24} - 186 q^{25} + 21 q^{26} + 16 q^{29} + 53 q^{30} + 24 q^{32} + 36 q^{33} - 86 q^{36} + 54 q^{37} + 39 q^{38} - 21 q^{40} - 27 q^{44} + 84 q^{45} + 41 q^{46} - 42 q^{50} + 69 q^{52} - 50 q^{53} - 36 q^{54} - 24 q^{57} - 11 q^{58} + 11 q^{60} - 6 q^{61} + 64 q^{64} + 28 q^{65} + 39 q^{66} + 75 q^{68} - 29 q^{72} + 18 q^{73} + 83 q^{74} - 292 q^{78} + 9 q^{80} + 162 q^{81} - 51 q^{82} - 136 q^{85} - 49 q^{86} - 25 q^{88} + 48 q^{89} + 168 q^{92} + 22 q^{93} - 99 q^{94} + 135 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)