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Properties

Label 2013.2.bo
Level $2013$
Weight $2$
Character orbit 2013.bo
Rep. character $\chi_{2013}(131,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $976$
Sturm bound $496$

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Defining parameters

Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2013.bo (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2013 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(496\)

Dimensions

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

Total New Old
Modular forms 1008 1008 0
Cusp forms 976 976 0
Eisenstein series 32 32 0

Trace form

\( 976 q - 6 q^{3} - 252 q^{4} - 6 q^{9} + O(q^{10}) \) \( 976 q - 6 q^{3} - 252 q^{4} - 6 q^{9} + 14 q^{12} - 18 q^{15} - 244 q^{16} - 30 q^{22} + 216 q^{25} - 12 q^{27} - 4 q^{31} + 19 q^{33} + 4 q^{34} - 14 q^{36} - 4 q^{37} + 74 q^{42} - 8 q^{45} + 160 q^{49} + 4 q^{55} - 20 q^{58} + 12 q^{60} - 216 q^{64} - 55 q^{66} + 28 q^{67} + 26 q^{69} - 40 q^{70} - 4 q^{75} - 76 q^{78} - 54 q^{81} - 16 q^{82} + 102 q^{88} + 96 q^{91} + 100 q^{93} + 28 q^{97} - 35 q^{99} + O(q^{100}) \)

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.