Properties

Label 115.3.f
Level $115$
Weight $3$
Character orbit 115.f
Rep. character $\chi_{115}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
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.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
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 52 44 8
Cusp forms 44 44 0
Eisenstein series 8 0 8

Trace form

\( 44q - 4q^{2} - 8q^{5} - 16q^{7} + 12q^{8} + O(q^{10}) \) \( 44q - 4q^{2} - 8q^{5} - 16q^{7} + 12q^{8} - 4q^{10} - 24q^{11} + 48q^{12} + 4q^{13} + 60q^{15} - 224q^{16} + 24q^{17} - 88q^{18} - 56q^{20} + 8q^{21} - 48q^{22} + 84q^{25} + 56q^{26} - 132q^{27} + 204q^{28} - 200q^{30} + 100q^{31} + 184q^{32} - 68q^{33} - 48q^{35} + 552q^{36} - 48q^{37} - 52q^{38} + 200q^{40} - 132q^{41} - 248q^{42} + 128q^{43} + 204q^{45} + 152q^{47} - 500q^{48} - 228q^{50} - 264q^{51} + 280q^{52} + 324q^{53} - 156q^{55} - 312q^{56} + 320q^{57} + 364q^{58} + 500q^{60} + 32q^{61} - 44q^{62} - 220q^{63} - 196q^{65} - 552q^{66} - 352q^{67} - 616q^{68} + 188q^{70} + 108q^{71} - 192q^{72} + 168q^{73} - 468q^{75} + 464q^{76} - 292q^{77} + 596q^{78} - 316q^{80} - 332q^{81} - 820q^{82} - 144q^{83} - 524q^{85} + 536q^{86} + 536q^{87} - 132q^{88} + 260q^{90} + 312q^{91} - 416q^{93} + 304q^{95} + 448q^{96} + 620q^{97} + 780q^{98} + O(q^{100}) \)

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.f.a \(44\) \(3.134\) None \(-4\) \(0\) \(-8\) \(-16\)