Properties

Label 130.2.n
Level $130$
Weight $2$
Character orbit 130.n
Rep. character $\chi_{130}(9,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 130.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 52 12 40
Cusp forms 36 12 24
Eisenstein series 16 0 16

Trace form

\( 12q + 6q^{4} - 2q^{9} + O(q^{10}) \) \( 12q + 6q^{4} - 2q^{9} - 2q^{10} - 6q^{11} + 20q^{14} + 4q^{15} - 6q^{16} - 26q^{19} - 24q^{21} + 4q^{25} - 28q^{29} - 16q^{30} + 24q^{31} - 16q^{34} - 6q^{35} + 2q^{36} + 36q^{39} - 4q^{40} - 4q^{41} - 12q^{44} + 12q^{45} - 4q^{49} - 8q^{50} + 8q^{51} + 12q^{54} + 12q^{55} + 10q^{56} + 16q^{59} + 8q^{60} - 8q^{61} - 12q^{64} - 10q^{65} - 24q^{66} + 28q^{69} + 24q^{70} + 40q^{71} - 10q^{74} - 8q^{75} + 26q^{76} + 56q^{79} + 26q^{81} - 12q^{84} - 16q^{85} + 24q^{86} + 14q^{89} + 20q^{90} - 38q^{91} - 14q^{94} - 8q^{95} - 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
130.2.n.a \(12\) \(1.038\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots\)

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

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