Properties

Label 115.2.l
Level $115$
Weight $2$
Character orbit 115.l
Rep. character $\chi_{115}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $200$
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.l (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
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 280 280 0
Cusp forms 200 200 0
Eisenstein series 80 80 0

Trace form

\( 200q - 18q^{2} - 14q^{3} - 22q^{5} - 36q^{6} - 22q^{7} - 26q^{8} + O(q^{10}) \) \( 200q - 18q^{2} - 14q^{3} - 22q^{5} - 36q^{6} - 22q^{7} - 26q^{8} - 22q^{10} - 44q^{11} - 6q^{12} - 26q^{13} - 22q^{15} - 52q^{16} - 22q^{17} + 58q^{18} - 22q^{20} - 44q^{21} + 22q^{23} - 10q^{25} - 28q^{26} - 26q^{27} + 66q^{28} - 22q^{30} - 40q^{31} - 46q^{32} - 14q^{35} - 12q^{36} + 66q^{37} - 22q^{38} - 22q^{40} - 8q^{41} + 198q^{42} - 22q^{43} - 76q^{46} + 52q^{47} + 18q^{48} - 82q^{50} - 44q^{51} + 158q^{52} - 22q^{53} - 10q^{55} + 88q^{56} + 66q^{57} - 58q^{58} - 22q^{60} + 44q^{61} + 38q^{62} - 22q^{63} - 22q^{65} + 132q^{66} - 22q^{67} + 32q^{70} + 132q^{71} - 28q^{72} + 34q^{73} + 38q^{75} + 132q^{76} - 10q^{77} + 22q^{78} + 176q^{80} - 48q^{81} - 50q^{82} - 22q^{83} + 202q^{85} - 46q^{87} - 110q^{88} + 396q^{90} + 50q^{92} - 36q^{93} + 68q^{95} + 148q^{96} - 88q^{97} - 50q^{98} + O(q^{100}) \)

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.l.a \(200\) \(0.918\) None \(-18\) \(-14\) \(-22\) \(-22\)