Properties

Label 115.3.i
Level $115$
Weight $3$
Character orbit 115.i
Rep. character $\chi_{115}(14,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $220$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 115.i (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(115, [\chi])\).

Total New Old
Modular forms 260 260 0
Cusp forms 220 220 0
Eisenstein series 40 40 0

Trace form

\( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} + O(q^{10}) \) \( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30} - 152 q^{31} - 264 q^{34} - 13 q^{35} - 62 q^{36} - 118 q^{39} - 11 q^{40} - 80 q^{41} - 242 q^{44} + 226 q^{46} + 90 q^{49} - 211 q^{50} - 22 q^{51} + 658 q^{54} - 565 q^{55} + 770 q^{56} - 172 q^{59} - 891 q^{60} + 286 q^{61} - 474 q^{64} - 242 q^{65} - 44 q^{66} - 288 q^{69} + 790 q^{70} - 210 q^{71} + 506 q^{74} + 804 q^{75} - 2376 q^{76} + 462 q^{79} + 2398 q^{80} - 2408 q^{81} + 1034 q^{84} + 1197 q^{85} - 1518 q^{86} - 22 q^{89} + 154 q^{90} - 210 q^{94} - 338 q^{95} + 2772 q^{96} + 1628 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.3.i.a $220$ $3.134$ None \(0\) \(0\) \(-11\) \(0\)