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Properties

Label 1205.2.bm
Level $1205$
Weight $2$
Character orbit 1205.bm
Rep. character $\chi_{1205}(729,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.bm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 960 q + 920 q^{4} - 10 q^{5} - 28 q^{6} - 260 q^{9} + O(q^{10}) \) \( 960 q + 920 q^{4} - 10 q^{5} - 28 q^{6} - 260 q^{9} - 10 q^{10} - 20 q^{11} - 36 q^{14} - 4 q^{15} + 856 q^{16} - 12 q^{19} - 70 q^{20} - 68 q^{21} - 96 q^{24} - 34 q^{25} - 72 q^{26} - 20 q^{29} - 56 q^{31} - 148 q^{34} + 42 q^{35} - 284 q^{36} - 20 q^{39} - 76 q^{40} - 20 q^{41} - 96 q^{44} + 20 q^{45} - 156 q^{46} - 20 q^{49} + 50 q^{50} - 20 q^{51} + 116 q^{54} - 44 q^{55} - 188 q^{56} - 20 q^{59} - 48 q^{60} + 40 q^{61} + 688 q^{64} - 28 q^{65} + 64 q^{66} + 60 q^{69} + 46 q^{70} + 16 q^{71} - 212 q^{74} - 90 q^{75} - 108 q^{76} + 100 q^{79} - 200 q^{80} - 136 q^{81} - 252 q^{84} - 14 q^{85} - 72 q^{86} - 40 q^{89} + 60 q^{90} + 84 q^{91} - 160 q^{94} - 76 q^{95} - 576 q^{96} + 104 q^{99} + O(q^{100}) \)

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.