Properties

Label 130.2.s
Level 130
Weight 2
Character orbit s
Rep. character \(\chi_{130}(33,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 28
Newforms 2
Sturm bound 42
Trace bound 1

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Defining parameters

Level: \( N \) = \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 130.s (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(130, [\chi])\).

Total New Old
Modular forms 100 28 72
Cusp forms 68 28 40
Eisenstein series 32 0 32

Trace form

\( 28q + 2q^{2} - 14q^{4} - 4q^{8} + 24q^{9} + O(q^{10}) \) \( 28q + 2q^{2} - 14q^{4} - 4q^{8} + 24q^{9} + 12q^{11} - 12q^{13} - 14q^{16} - 2q^{17} - 36q^{19} - 24q^{21} + 26q^{25} - 24q^{27} - 12q^{30} - 24q^{31} + 2q^{32} + 44q^{33} + 26q^{34} - 12q^{35} - 24q^{36} - 18q^{37} - 26q^{41} + 12q^{42} - 12q^{44} - 72q^{45} - 12q^{46} + 2q^{49} + 28q^{50} - 6q^{53} - 32q^{55} + 12q^{56} + 64q^{57} + 12q^{58} + 28q^{59} + 24q^{60} + 24q^{61} + 48q^{62} + 28q^{64} + 66q^{65} + 16q^{66} + 56q^{67} + 4q^{68} - 16q^{69} + 24q^{70} + 24q^{71} + 24q^{72} - 28q^{73} - 30q^{74} + 88q^{75} + 24q^{76} - 88q^{77} + 36q^{78} + 6q^{81} - 28q^{82} - 58q^{85} - 80q^{87} + 18q^{89} + 30q^{90} + 32q^{91} - 36q^{93} - 24q^{94} - 24q^{95} + 20q^{97} - 2q^{98} - 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
130.2.s.a \(12\) \(1.038\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(0\) \(6\) \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots\)
130.2.s.b \(16\) \(1.038\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(0\) \(0\) \(-6\) \(q+(1+\beta _{8})q^{2}+(\beta _{2}-\beta _{11})q^{3}+\beta _{8}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(130, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)