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Properties

Label 1205.2.v
Level $1205$
Weight $2$
Character orbit 1205.v
Rep. character $\chi_{1205}(36,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $328$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 488 328 160
Cusp forms 472 328 144
Eisenstein series 16 0 16

Trace form

\( 328 q - 8 q^{2} + 8 q^{3} + 340 q^{4} + 2 q^{5} - 6 q^{6} - 24 q^{8} - 102 q^{9} + O(q^{10}) \) \( 328 q - 8 q^{2} + 8 q^{3} + 340 q^{4} + 2 q^{5} - 6 q^{6} - 24 q^{8} - 102 q^{9} - 8 q^{10} + 4 q^{12} - 50 q^{13} + 16 q^{15} + 364 q^{16} + 30 q^{18} + 6 q^{20} - 50 q^{21} - 14 q^{24} - 82 q^{25} - 22 q^{27} - 4 q^{29} - 20 q^{30} + 40 q^{31} - 36 q^{32} - 20 q^{33} + 60 q^{34} - 10 q^{35} - 178 q^{36} - 10 q^{37} - 2 q^{40} - 12 q^{41} + 50 q^{42} - 100 q^{43} - 12 q^{45} + 20 q^{46} - 12 q^{47} + 8 q^{48} + 98 q^{49} + 2 q^{50} + 10 q^{51} - 140 q^{52} + 12 q^{54} + 20 q^{55} - 70 q^{56} + 40 q^{57} - 94 q^{58} - 10 q^{59} + 28 q^{60} + 42 q^{61} + 20 q^{62} + 280 q^{64} - 70 q^{66} + 42 q^{67} - 50 q^{68} + 30 q^{69} - 30 q^{70} - 40 q^{71} + 70 q^{72} + 10 q^{73} - 20 q^{74} + 8 q^{75} + 6 q^{77} - 80 q^{78} - 34 q^{79} + 38 q^{80} - 74 q^{81} + 16 q^{82} + 30 q^{83} - 220 q^{84} - 40 q^{85} - 90 q^{86} + 16 q^{87} + 2 q^{90} - 24 q^{91} + 60 q^{92} + 28 q^{94} - 60 q^{96} + 98 q^{97} - 46 q^{98} + 10 q^{99} + O(q^{100}) \)

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

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