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Properties

Label 1848.2.ep
Level $1848$
Weight $2$
Character orbit 1848.ep
Rep. character $\chi_{1848}(149,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3008$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.ep (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1848 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 3136 3136 0
Cusp forms 3008 3008 0
Eisenstein series 128 128 0

Trace form

\( 3008 q - 6 q^{4} - 20 q^{6} - 40 q^{7} - 6 q^{9} + O(q^{10}) \) \( 3008 q - 6 q^{4} - 20 q^{6} - 40 q^{7} - 6 q^{9} + 4 q^{12} - 48 q^{15} + 10 q^{16} - 5 q^{18} - 88 q^{22} - 5 q^{24} + 332 q^{25} - 20 q^{28} + 25 q^{30} - 12 q^{31} - 20 q^{33} - 32 q^{34} - 48 q^{36} - 10 q^{39} - 10 q^{40} - 118 q^{42} - 50 q^{46} + 106 q^{48} - 24 q^{49} - 10 q^{52} - 104 q^{55} - 40 q^{57} + 14 q^{58} - q^{60} - 20 q^{63} + 96 q^{64} - 45 q^{66} - 102 q^{70} - 5 q^{72} - 20 q^{73} - 84 q^{78} + 140 q^{79} - 6 q^{81} + 26 q^{82} + 45 q^{84} - 28 q^{88} - 90 q^{90} - 130 q^{94} - 105 q^{96} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

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