Properties

Label 115.2.j
Level $115$
Weight $2$
Character orbit 115.j
Rep. character $\chi_{115}(4,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $100$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.j (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(115, [\chi])\).

Total New Old
Modular forms 140 140 0
Cusp forms 100 100 0
Eisenstein series 40 40 0

Trace form

\( 100q - 14q^{4} - 9q^{5} - 18q^{6} - 12q^{9} + O(q^{10}) \) \( 100q - 14q^{4} - 9q^{5} - 18q^{6} - 12q^{9} - 13q^{10} - 26q^{11} - 26q^{14} - 10q^{15} - 18q^{16} - 14q^{19} + 49q^{20} - 22q^{21} - 68q^{24} + 21q^{25} - 42q^{26} - 24q^{29} + 19q^{30} - 12q^{31} + 8q^{34} - 37q^{35} - 10q^{36} + 14q^{39} - q^{40} + 8q^{41} + 166q^{44} - 42q^{45} - 18q^{46} + 32q^{49} - 23q^{50} - 22q^{51} + 116q^{54} + 27q^{55} - 116q^{56} + 50q^{59} + 123q^{60} - 38q^{61} + 10q^{64} + 76q^{65} - 28q^{66} + 80q^{69} + 102q^{70} - 110q^{71} + 22q^{74} + 6q^{75} + 4q^{76} + 42q^{79} + 18q^{80} + 204q^{81} + 56q^{84} - 121q^{85} + 132q^{86} - 66q^{89} - 198q^{90} + 76q^{91} - 70q^{94} - 74q^{95} + 236q^{96} - 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
115.2.j.a \(100\) \(0.918\) None \(0\) \(0\) \(-9\) \(0\)