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Properties

Label 2156.2.bl
Level $2156$
Weight $2$
Character orbit 2156.bl
Rep. character $\chi_{2156}(79,\cdot)$
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.bl (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

\( 1856 q + 5 q^{2} + 7 q^{4} + 6 q^{5} + 20 q^{6} - 40 q^{8} - 210 q^{9} + O(q^{10}) \) \( 1856 q + 5 q^{2} + 7 q^{4} + 6 q^{5} + 20 q^{6} - 40 q^{8} - 210 q^{9} - 4 q^{12} + 40 q^{13} + 19 q^{16} + 10 q^{17} + 55 q^{18} + 20 q^{20} + 44 q^{22} - 25 q^{24} + 198 q^{25} + 15 q^{26} - 80 q^{29} + 65 q^{30} - 8 q^{33} - 56 q^{34} + 30 q^{36} + 54 q^{37} + 21 q^{38} + 5 q^{40} + 80 q^{41} - 27 q^{44} + 68 q^{45} - 105 q^{46} - 26 q^{48} + 10 q^{50} + 5 q^{52} + 46 q^{53} - 80 q^{57} + 5 q^{58} + 59 q^{60} + 10 q^{61} + 20 q^{62} + 16 q^{64} - 43 q^{66} + 5 q^{68} + 28 q^{69} - 45 q^{72} - 30 q^{73} - 65 q^{74} + 84 q^{78} - 43 q^{80} + 186 q^{81} + 31 q^{82} + 80 q^{85} + 119 q^{86} - 11 q^{88} + 90 q^{90} - 128 q^{92} - 10 q^{93} - 115 q^{94} - 95 q^{96} - 56 q^{97} + O(q^{100}) \)

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

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