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Properties

Label 1805.2.e
Level $1805$
Weight $2$
Character orbit 1805.e
Rep. character $\chi_{1805}(1151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $224$
Sturm bound $380$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(380\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1805, [\chi])\).

Total New Old
Modular forms 420 224 196
Cusp forms 340 224 116
Eisenstein series 80 0 80

Trace form

\( 224 q + 2 q^{2} + 2 q^{3} - 110 q^{4} - 4 q^{6} + 12 q^{7} - 12 q^{8} - 114 q^{9} + O(q^{10}) \) \( 224 q + 2 q^{2} + 2 q^{3} - 110 q^{4} - 4 q^{6} + 12 q^{7} - 12 q^{8} - 114 q^{9} + 8 q^{11} - 12 q^{12} - 6 q^{13} + 6 q^{14} + 4 q^{15} - 106 q^{16} + 6 q^{17} - 8 q^{18} - 8 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - 112 q^{25} - 12 q^{26} - 16 q^{27} - 6 q^{29} - 32 q^{30} + 16 q^{31} + 24 q^{32} + 24 q^{33} - 10 q^{34} - 2 q^{35} - 118 q^{36} - 8 q^{37} - 36 q^{39} + 18 q^{40} - 16 q^{41} - 26 q^{42} - 4 q^{43} - 28 q^{44} + 8 q^{45} + 24 q^{46} + 12 q^{47} + 16 q^{48} + 256 q^{49} - 4 q^{50} + 4 q^{51} - 42 q^{52} - 4 q^{54} + 52 q^{56} + 52 q^{58} - 14 q^{59} + 6 q^{60} + 4 q^{61} + 36 q^{62} + 14 q^{63} + 136 q^{64} - 40 q^{65} + 14 q^{66} - 14 q^{67} - 100 q^{68} + 28 q^{69} - 8 q^{70} - 12 q^{71} + 28 q^{72} - 26 q^{73} + 42 q^{74} - 4 q^{75} + 28 q^{77} + 12 q^{78} - 2 q^{79} + 8 q^{80} - 132 q^{81} + 72 q^{82} - 36 q^{83} + 128 q^{84} - 8 q^{85} - 24 q^{86} - 44 q^{87} + 32 q^{88} - 18 q^{89} - 24 q^{90} - 12 q^{91} + 52 q^{92} + 28 q^{93} + 20 q^{94} - 124 q^{96} + 16 q^{97} + 32 q^{98} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 2}\)