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Properties

Label 1205.2.m
Level $1205$
Weight $2$
Character orbit 1205.m
Rep. character $\chi_{1205}(16,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1205, [\chi])\).

Total New Old
Modular forms 244 160 84
Cusp forms 236 160 76
Eisenstein series 8 0 8

Trace form

\( 160 q + 2 q^{2} + 6 q^{3} - 76 q^{4} - 4 q^{5} + 16 q^{6} - 12 q^{8} - 88 q^{9} + O(q^{10}) \) \( 160 q + 2 q^{2} + 6 q^{3} - 76 q^{4} - 4 q^{5} + 16 q^{6} - 12 q^{8} - 88 q^{9} - 4 q^{10} - 4 q^{12} + 12 q^{13} + 30 q^{14} - 4 q^{15} - 68 q^{16} - 18 q^{19} + 6 q^{20} - 18 q^{22} - 40 q^{24} + 160 q^{25} - 72 q^{27} + 20 q^{29} - 12 q^{30} + 54 q^{31} + 4 q^{32} + 6 q^{34} + 88 q^{36} - 18 q^{37} - 6 q^{38} + 6 q^{39} - 12 q^{40} + 24 q^{41} - 6 q^{42} - 30 q^{46} - 44 q^{47} + 120 q^{48} + 76 q^{49} + 2 q^{50} - 78 q^{51} + 24 q^{52} + 8 q^{53} - 24 q^{54} + 42 q^{56} + 8 q^{58} - 6 q^{59} - 6 q^{60} - 60 q^{61} - 126 q^{62} + 48 q^{63} + 140 q^{64} - 18 q^{65} + 12 q^{66} + 14 q^{67} - 48 q^{68} + 6 q^{69} - 30 q^{71} + 10 q^{72} - 24 q^{74} + 6 q^{75} + 36 q^{77} + 48 q^{78} - 12 q^{79} + 22 q^{80} - 92 q^{81} + 10 q^{82} - 48 q^{83} - 84 q^{84} - 6 q^{86} + 68 q^{87} + 66 q^{88} + 24 q^{89} - 36 q^{90} - 12 q^{91} + 48 q^{92} + 24 q^{94} - 70 q^{96} - 8 q^{97} + 8 q^{98} - 150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(241, [\chi])\)\(^{\oplus 2}\)