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Properties

Label 1205.2.bt
Level $1205$
Weight $2$
Character orbit 1205.bt
Rep. character $\chi_{1205}(299,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $960$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.bt (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 992 992 0
Cusp forms 960 960 0
Eisenstein series 32 32 0

Trace form

\( 960 q + 470 q^{4} - 8 q^{5} - 34 q^{6} - 140 q^{9} + O(q^{10}) \) \( 960 q + 470 q^{4} - 8 q^{5} - 34 q^{6} - 140 q^{9} - 25 q^{10} - 30 q^{11} - 34 q^{14} + 7 q^{15} - 466 q^{16} - 30 q^{19} - 23 q^{20} - 20 q^{21} + 86 q^{24} + 10 q^{26} - 26 q^{29} - 2 q^{30} - 42 q^{31} + 32 q^{34} - 29 q^{35} - 264 q^{36} - 2 q^{39} - 30 q^{40} + 68 q^{41} - 51 q^{45} - 14 q^{46} + 82 q^{49} + 80 q^{50} + 4 q^{51} - 24 q^{54} + 22 q^{55} + 116 q^{56} - 16 q^{59} - 13 q^{60} + 78 q^{61} - 920 q^{64} - 84 q^{65} + 8 q^{66} + 6 q^{69} - 6 q^{70} - 62 q^{71} + 52 q^{74} + 101 q^{75} + 28 q^{79} + 23 q^{80} + 72 q^{81} - 124 q^{84} - 5 q^{85} - 144 q^{86} + 90 q^{89} + 173 q^{90} - 116 q^{91} + 112 q^{94} - 20 q^{95} + 412 q^{96} - 100 q^{99} + O(q^{100}) \)

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.