Properties

Label 115.2.e
Level $115$
Weight $2$
Character orbit 115.e
Rep. character $\chi_{115}(22,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
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.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
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 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20q - 4q^{2} - 8q^{3} - 8q^{6} + 4q^{8} + O(q^{10}) \) \( 20q - 4q^{2} - 8q^{3} - 8q^{6} + 4q^{8} - 16q^{12} + 4q^{13} + 8q^{16} + 8q^{18} - 12q^{25} - 16q^{26} + 4q^{27} - 4q^{31} + 24q^{32} - 8q^{35} - 32q^{36} - 36q^{41} + 32q^{46} - 8q^{47} + 4q^{48} + 60q^{50} + 40q^{52} - 12q^{55} + 36q^{58} - 60q^{62} - 76q^{70} + 44q^{71} + 72q^{72} - 56q^{73} + 28q^{75} - 12q^{77} - 44q^{78} + 92q^{81} + 28q^{82} - 4q^{85} + 24q^{87} - 72q^{92} - 8q^{93} + 64q^{95} - 104q^{96} - 60q^{98} + O(q^{100}) \)

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.e.a \(20\) \(0.918\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-8\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+\beta _{4}q^{4}+\beta _{18}q^{5}+\cdots\)