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Properties

Label 2013.2.da
Level $2013$
Weight $2$
Character orbit 2013.da
Rep. character $\chi_{2013}(191,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1952$
Sturm bound $496$

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Defining parameters

Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2013.da (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2013 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(496\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2013, [\chi])\).

Total New Old
Modular forms 2016 2016 0
Cusp forms 1952 1952 0
Eisenstein series 64 64 0

Trace form

\( 1952 q - 10 q^{3} - 18 q^{6} - 12 q^{7} - 2 q^{9} + O(q^{10}) \) \( 1952 q - 10 q^{3} - 18 q^{6} - 12 q^{7} - 2 q^{9} - 32 q^{10} - 6 q^{12} - 24 q^{13} + 22 q^{15} - 1912 q^{16} - 14 q^{18} - 20 q^{19} - 40 q^{21} - 12 q^{22} - 10 q^{24} - 460 q^{25} + 20 q^{27} + 132 q^{28} + 26 q^{30} - 20 q^{31} - 24 q^{33} - 24 q^{34} + 70 q^{36} - 4 q^{37} - 60 q^{39} + 28 q^{40} + 12 q^{42} + 24 q^{43} - 20 q^{45} - 20 q^{46} + 10 q^{48} + 20 q^{49} + 18 q^{51} + 60 q^{52} - 70 q^{54} + 4 q^{55} - 10 q^{57} + 52 q^{58} + 50 q^{60} - 12 q^{61} - 8 q^{63} + 300 q^{66} - 32 q^{67} - 8 q^{69} + 104 q^{70} - 152 q^{72} - 50 q^{75} - 40 q^{76} - 146 q^{78} + 4 q^{79} + 46 q^{81} + 36 q^{82} + 94 q^{84} + 44 q^{85} + 96 q^{87} + 340 q^{88} - 256 q^{90} + 20 q^{91} - 36 q^{93} - 148 q^{94} - 94 q^{96} - 20 q^{97} - 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2013, [\chi])\) into newform subspaces

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