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Properties

Label 2013.2.cl
Level $2013$
Weight $2$
Character orbit 2013.cl
Rep. character $\chi_{2013}(796,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $496$
Sturm bound $496$

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Defining parameters

Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2013.cl (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 671 \)
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 496 512
Cusp forms 976 496 480
Eisenstein series 32 0 32

Trace form

\( 496 q + 124 q^{4} - 12 q^{5} - 124 q^{9} + O(q^{10}) \) \( 496 q + 124 q^{4} - 12 q^{5} - 124 q^{9} + 10 q^{11} - 4 q^{12} + 8 q^{13} - 4 q^{14} - 140 q^{16} - 16 q^{19} - 32 q^{20} - 4 q^{22} - 20 q^{23} + 508 q^{25} - 20 q^{29} - 20 q^{31} - 10 q^{33} - 10 q^{34} - 40 q^{35} - 496 q^{36} + 10 q^{37} - 16 q^{39} - 20 q^{43} + 8 q^{45} + 80 q^{46} - 12 q^{47} - 16 q^{48} + 124 q^{49} - 40 q^{50} - 20 q^{51} - 42 q^{52} - 20 q^{55} - 48 q^{56} + 12 q^{57} - 36 q^{58} + 36 q^{60} + 36 q^{61} - 8 q^{62} + 180 q^{64} + 32 q^{65} + 28 q^{66} - 40 q^{67} + 20 q^{68} - 20 q^{69} + 60 q^{71} + 6 q^{73} + 20 q^{74} + 12 q^{75} + 24 q^{76} + 52 q^{77} - 102 q^{80} - 124 q^{81} + 40 q^{82} - 14 q^{83} - 56 q^{86} - 130 q^{88} - 40 q^{89} - 160 q^{92} - 60 q^{93} - 80 q^{94} - 58 q^{95} + 48 q^{97} - 180 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2013, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2013, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(671, [\chi])\)\(^{\oplus 2}\)