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Properties

Label 1175.2.u
Level $1175$
Weight $2$
Character orbit 1175.u
Rep. character $\chi_{1175}(4,\cdot)$
Character field $\Q(\zeta_{230})$
Dimension $10384$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1175.u (of order \(230\) and degree \(88\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{230})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1175, [\chi])\).

Total New Old
Modular forms 10736 10736 0
Cusp forms 10384 10384 0
Eisenstein series 352 352 0

Trace form

\( 10384 q - 105 q^{2} - 105 q^{3} - 179 q^{4} - 94 q^{5} - 55 q^{6} - 135 q^{8} - 181 q^{9} + O(q^{10}) \) \( 10384 q - 105 q^{2} - 105 q^{3} - 179 q^{4} - 94 q^{5} - 55 q^{6} - 135 q^{8} - 181 q^{9} - 82 q^{10} - 61 q^{11} - 145 q^{12} - 105 q^{13} - 87 q^{14} - 84 q^{15} + 33 q^{16} - 95 q^{17} - 71 q^{19} - 82 q^{20} - 81 q^{21} - 105 q^{22} - 125 q^{23} - 164 q^{24} - 58 q^{25} - 208 q^{26} - 75 q^{27} - 145 q^{28} - 63 q^{29} - 92 q^{30} - 39 q^{31} - 105 q^{33} - 55 q^{34} - 226 q^{35} - 139 q^{36} - 105 q^{37} - 75 q^{38} - 67 q^{39} - 10 q^{40} + 142 q^{41} - 165 q^{42} - 65 q^{44} + 59 q^{45} - 300 q^{46} - 115 q^{47} - 300 q^{48} + 236 q^{49} + 10 q^{50} - 342 q^{51} + 5 q^{52} - 125 q^{53} - 121 q^{54} - 3 q^{55} + 301 q^{56} - 155 q^{58} - 69 q^{59} - 376 q^{60} - 129 q^{61} - 45 q^{62} - 225 q^{63} - 177 q^{64} - 18 q^{65} - 3 q^{66} - 155 q^{67} - 137 q^{69} - 90 q^{70} - 107 q^{71} - 265 q^{72} - 185 q^{73} - 160 q^{74} - 114 q^{75} - 196 q^{76} - 175 q^{77} - 135 q^{78} - 71 q^{79} - 405 q^{80} + 13 q^{81} - 65 q^{83} - 201 q^{84} - 282 q^{85} - 55 q^{86} - 155 q^{87} + 95 q^{88} - 43 q^{89} - 348 q^{90} - 81 q^{91} - 155 q^{92} - 264 q^{94} - 350 q^{95} + 153 q^{96} - 105 q^{97} - 55 q^{98} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1175, [\chi])\) into newform subspaces

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