↑

Properties

Label 1205.2.l
Level $1205$
Weight $2$
Character orbit 1205.l
Rep. character $\chi_{1205}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $328$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

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

\( 328 q + 8 q^{2} - 8 q^{3} + 340 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 102 q^{9} + O(q^{10}) \) \( 328 q + 8 q^{2} - 8 q^{3} + 340 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 102 q^{9} + 4 q^{10} - 8 q^{11} - 44 q^{12} + 30 q^{13} - 8 q^{14} + 16 q^{15} + 364 q^{16} - 16 q^{17} - 30 q^{18} + 20 q^{19} - 6 q^{20} + 6 q^{21} - 36 q^{22} - 16 q^{23} - 10 q^{24} - 82 q^{25} - 4 q^{26} - 26 q^{27} - 64 q^{28} - 28 q^{29} + 12 q^{30} - 8 q^{31} + 36 q^{32} + 48 q^{33} - 4 q^{34} + 6 q^{35} - 58 q^{36} - 30 q^{37} - 24 q^{38} - 36 q^{39} - 10 q^{40} + 4 q^{41} - 34 q^{42} + 48 q^{43} - 24 q^{44} + 12 q^{45} - 16 q^{46} - 4 q^{47} - 168 q^{48} - 98 q^{49} - 2 q^{50} - 26 q^{51} + 28 q^{52} - 32 q^{54} + 12 q^{55} - 2 q^{56} + 44 q^{57} + 86 q^{58} + 18 q^{59} + 28 q^{60} - 22 q^{61} - 64 q^{62} + 104 q^{63} + 472 q^{64} + 64 q^{65} + 42 q^{66} - 38 q^{67} - 66 q^{68} - 38 q^{69} + 18 q^{70} + 20 q^{71} - 70 q^{72} - 66 q^{73} - 32 q^{74} - 8 q^{75} + 44 q^{76} - 6 q^{77} - 40 q^{78} + 10 q^{79} + 10 q^{80} - 90 q^{81} + 16 q^{82} + 34 q^{83} + 36 q^{84} + 24 q^{85} - 46 q^{86} - 56 q^{87} - 116 q^{88} - 92 q^{89} - 22 q^{90} - 32 q^{91} - 68 q^{92} - 120 q^{93} - 16 q^{94} - 68 q^{96} - 6 q^{97} + 2 q^{98} - 78 q^{99} + O(q^{100}) \)

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

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