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Properties

Label 2028.2.be
Level $2028$
Weight $2$
Character orbit 2028.be
Rep. character $\chi_{2028}(131,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $4320$
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.be (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2028 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 4416 4416 0
Cusp forms 4320 4320 0
Eisenstein series 96 96 0

Trace form

\( 4320 q - 22 q^{4} - 13 q^{6} - 22 q^{9} + O(q^{10}) \) \( 4320 q - 22 q^{4} - 13 q^{6} - 22 q^{9} - 30 q^{10} - 23 q^{12} - 22 q^{16} - 48 q^{18} - 34 q^{21} - 28 q^{22} + 11 q^{24} + 300 q^{25} - 26 q^{28} - 7 q^{30} - 10 q^{33} - 42 q^{34} - 13 q^{36} - 52 q^{37} - 62 q^{40} - 21 q^{42} - 42 q^{45} - 70 q^{46} - 24 q^{48} + 316 q^{49} - 22 q^{52} + 3 q^{54} + 28 q^{57} - 58 q^{58} - 49 q^{60} - 20 q^{61} + 26 q^{64} + 92 q^{66} - 72 q^{69} - 92 q^{70} + 144 q^{72} - 68 q^{73} + 134 q^{76} - 3 q^{78} - 6 q^{81} + 136 q^{82} + 194 q^{84} - 172 q^{85} - 10 q^{88} + 41 q^{90} - 2 q^{93} + 88 q^{94} - 206 q^{96} - 68 q^{97} + O(q^{100}) \)

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.