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Properties

Label 2075.2.t
Level $2075$
Weight $2$
Character orbit 2075.t
Rep. character $\chi_{2075}(4,\cdot)$
Character field $\Q(\zeta_{410})$
Dimension $33280$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2075.t (of order \(410\) and degree \(160\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2075 \)
Character field: \(\Q(\zeta_{410})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 33920 33920 0
Cusp forms 33280 33280 0
Eisenstein series 640 640 0

Trace form

\( 33280 q - 195 q^{2} - 195 q^{3} - 323 q^{4} - 158 q^{5} - 105 q^{6} - 195 q^{8} - 321 q^{9} + O(q^{10}) \) \( 33280 q - 195 q^{2} - 195 q^{3} - 323 q^{4} - 158 q^{5} - 105 q^{6} - 195 q^{8} - 321 q^{9} - 164 q^{10} - 123 q^{11} - 195 q^{12} - 195 q^{13} - 137 q^{14} - 186 q^{15} + 69 q^{16} - 185 q^{17} - 125 q^{19} - 148 q^{20} - 135 q^{21} - 245 q^{22} - 215 q^{23} - 288 q^{24} - 142 q^{25} - 284 q^{26} - 195 q^{27} - 175 q^{28} - 105 q^{29} - 142 q^{30} - 129 q^{31} - 195 q^{33} - 117 q^{34} - 174 q^{35} + 65 q^{36} - 195 q^{37} - 265 q^{38} - 97 q^{39} - 190 q^{40} - 135 q^{41} - 275 q^{42} - 141 q^{44} - 160 q^{45} - 61 q^{46} - 205 q^{47} - 175 q^{48} + 428 q^{49} - 154 q^{50} - 280 q^{51} - 275 q^{52} - 215 q^{53} - 167 q^{54} - 126 q^{55} - 143 q^{56} - 195 q^{58} - 105 q^{59} - 334 q^{60} - 137 q^{61} - 145 q^{62} - 275 q^{63} - 291 q^{64} - 112 q^{65} - 179 q^{66} - 155 q^{67} - 63 q^{69} - 376 q^{70} - 113 q^{71} - 65 q^{72} - 155 q^{73} - 296 q^{74} + 988 q^{75} - 380 q^{76} - 185 q^{77} - 2115 q^{78} - 153 q^{79} - 612 q^{80} + 47 q^{81} + 455 q^{83} - 378 q^{84} - 283 q^{85} - 129 q^{86} - 145 q^{87} - 285 q^{88} - 153 q^{89} - 632 q^{90} - 99 q^{91} - 315 q^{92} + 7 q^{94} - 317 q^{95} - 231 q^{96} - 85 q^{97} - 245 q^{98} - 428 q^{99} + O(q^{100}) \)

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.