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Properties

Label 2075.2.g
Level $2075$
Weight $2$
Character orbit 2075.g
Rep. character $\chi_{2075}(416,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $824$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2075.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2075, [\chi])\).

Total New Old
Modular forms 848 824 24
Cusp forms 832 824 8
Eisenstein series 16 0 16

Trace form

\( 824 q - 2 q^{2} - 4 q^{3} - 208 q^{4} + 4 q^{5} + 12 q^{8} - 214 q^{9} + O(q^{10}) \) \( 824 q - 2 q^{2} - 4 q^{3} - 208 q^{4} + 4 q^{5} + 12 q^{8} - 214 q^{9} - 12 q^{10} - 8 q^{11} + 24 q^{12} - 24 q^{13} - 12 q^{14} - 20 q^{15} - 212 q^{16} - 28 q^{17} + 40 q^{18} + 12 q^{19} + 26 q^{20} - 20 q^{21} + 24 q^{22} - 4 q^{23} + 20 q^{25} + 36 q^{26} - 4 q^{27} - 44 q^{28} - 28 q^{29} + 52 q^{30} - 24 q^{31} - 8 q^{32} + 14 q^{33} - 2 q^{34} - 40 q^{35} - 176 q^{36} + 20 q^{37} - 34 q^{38} - 20 q^{39} - 60 q^{40} - 40 q^{41} + 4 q^{42} - 8 q^{43} + 22 q^{44} + 48 q^{45} + 24 q^{46} - 40 q^{47} + 106 q^{48} + 856 q^{49} + 50 q^{50} + 40 q^{51} - 22 q^{52} - 24 q^{53} + 54 q^{54} - 26 q^{55} + 100 q^{57} + 54 q^{58} - 18 q^{59} + 2 q^{60} - 52 q^{61} + 36 q^{62} - 18 q^{63} - 250 q^{64} + 16 q^{65} - 32 q^{66} + 6 q^{67} + 76 q^{68} - 34 q^{69} - 124 q^{70} - 18 q^{71} + 20 q^{72} + 8 q^{73} - 28 q^{74} - 56 q^{75} - 92 q^{76} - 32 q^{77} + 34 q^{78} - 112 q^{80} - 224 q^{81} - 136 q^{82} + 96 q^{84} + 4 q^{85} - 24 q^{86} + 72 q^{87} + 24 q^{88} + 70 q^{89} + 46 q^{90} + 36 q^{91} + 62 q^{92} + 144 q^{93} - 76 q^{94} - 80 q^{95} - 76 q^{96} - 108 q^{97} + 102 q^{98} + 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2075, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2075, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2075, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)