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Properties

Label 1205.2.ch
Level $1205$
Weight $2$
Character orbit 1205.ch
Rep. character $\chi_{1205}(96,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1280$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.ch (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 1952 1280 672
Cusp forms 1888 1280 608
Eisenstein series 64 0 64

Trace form

\( 1280 q + 620 q^{4} - 16 q^{6} + 4 q^{7} - 184 q^{9} + O(q^{10}) \) \( 1280 q + 620 q^{4} - 16 q^{6} + 4 q^{7} - 184 q^{9} + 4 q^{10} + 4 q^{11} + 20 q^{13} - 52 q^{14} - 32 q^{15} - 588 q^{16} + 28 q^{17} + 72 q^{19} + 4 q^{21} + 48 q^{22} - 20 q^{23} - 24 q^{24} + 320 q^{25} + 4 q^{26} - 24 q^{28} + 24 q^{29} + 8 q^{31} - 76 q^{33} - 56 q^{34} - 4 q^{35} - 368 q^{36} - 12 q^{37} - 24 q^{38} - 4 q^{39} + 24 q^{40} + 184 q^{42} + 8 q^{43} + 24 q^{44} - 4 q^{46} + 72 q^{49} + 96 q^{51} - 88 q^{52} + 52 q^{54} + 32 q^{55} + 20 q^{56} + 220 q^{57} + 8 q^{58} + 52 q^{59} + 60 q^{60} + 60 q^{61} + 12 q^{62} - 352 q^{63} - 1056 q^{64} + 32 q^{65} - 64 q^{66} + 60 q^{67} - 48 q^{68} + 60 q^{69} + 12 q^{70} - 12 q^{71} - 112 q^{73} + 60 q^{74} - 140 q^{76} - 80 q^{78} + 112 q^{80} - 44 q^{81} - 172 q^{82} + 76 q^{83} + 128 q^{84} + 32 q^{85} - 72 q^{86} - 8 q^{87} + 196 q^{88} - 80 q^{89} - 20 q^{90} + 32 q^{91} - 192 q^{92} + 76 q^{93} + 36 q^{94} + 92 q^{96} - 340 q^{97} - 64 q^{98} + 156 q^{99} + O(q^{100}) \)

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

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