Properties

Label 115.2.b
Level $115$
Weight $2$
Character orbit 115.b
Rep. character $\chi_{115}(24,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 14 10 4
Cusp forms 10 10 0
Eisenstein series 4 0 4

Trace form

\( 10q - 8q^{4} - 2q^{5} - 4q^{6} - 10q^{9} + O(q^{10}) \) \( 10q - 8q^{4} - 2q^{5} - 4q^{6} - 10q^{9} + 2q^{10} + 4q^{11} + 4q^{14} + 10q^{15} - 4q^{16} - 8q^{19} - 16q^{20} + 24q^{24} - 10q^{25} + 20q^{26} + 2q^{29} + 14q^{30} - 10q^{31} - 8q^{34} + 26q^{35} - 12q^{36} + 8q^{39} - 10q^{40} - 30q^{41} - 12q^{44} + 20q^{45} - 4q^{46} + 12q^{49} + 12q^{50} - 28q^{54} - 16q^{55} + 28q^{56} - 6q^{59} - 24q^{60} - 28q^{61} + 56q^{64} - 10q^{65} - 16q^{66} + 8q^{69} - 36q^{70} - 22q^{71} + 44q^{74} + 16q^{75} - 4q^{76} - 20q^{79} - 18q^{80} - 6q^{81} - 12q^{84} + 22q^{85} + 44q^{86} + 44q^{89} + 56q^{91} + 92q^{94} - 36q^{95} + 28q^{96} - 72q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.918\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\)
115.2.b.b \(8\) \(0.918\) 8.0.527896576.2 None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)