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Properties

Label 2028.2.bn
Level $2028$
Weight $2$
Character orbit 2028.bn
Rep. character $\chi_{2028}(95,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $8640$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2028.bn (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2028 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2028, [\chi])\).

Total New Old
Modular forms 8832 8832 0
Cusp forms 8640 8640 0
Eisenstein series 192 192 0

Trace form

\( 8640 q - 50 q^{4} - 14 q^{6} - 50 q^{9} + O(q^{10}) \) \( 8640 q - 50 q^{4} - 14 q^{6} - 50 q^{9} - 46 q^{10} - 22 q^{12} - 48 q^{13} - 50 q^{16} + 52 q^{18} - 52 q^{21} - 22 q^{22} - 8 q^{24} - 776 q^{25} - 64 q^{28} - 2 q^{30} - 46 q^{33} - 52 q^{34} - 22 q^{36} - 68 q^{37} + 16 q^{40} - 32 q^{42} - 16 q^{45} - 24 q^{46} - 65 q^{48} + 248 q^{49} - 104 q^{52} - 56 q^{54} + 26 q^{57} - 106 q^{58} - 26 q^{60} - 96 q^{61} - 80 q^{64} - 197 q^{66} + 8 q^{69} + 131 q^{72} - 104 q^{73} - 156 q^{76} - 88 q^{78} - 58 q^{81} - 236 q^{82} + 95 q^{84} - 136 q^{85} - 72 q^{88} - 78 q^{90} - 52 q^{93} - 102 q^{94} + 143 q^{96} - 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

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