Properties

Label 130.2.b
Level $130$
Weight $2$
Character orbit 130.b
Rep. character $\chi_{130}(79,\cdot)$
Character field $\Q$
Dimension $6$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 26 6 20
Cusp forms 18 6 12
Eisenstein series 8 0 8

Trace form

\( 6 q - 6 q^{4} - 10 q^{9} + O(q^{10}) \) \( 6 q - 6 q^{4} - 10 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{14} - 16 q^{15} + 6 q^{16} - 4 q^{19} + 24 q^{21} - 16 q^{25} + 6 q^{26} + 4 q^{29} - 14 q^{30} + 24 q^{31} - 8 q^{34} - 6 q^{35} + 10 q^{36} + 4 q^{40} + 4 q^{41} - 12 q^{44} - 12 q^{45} + 12 q^{46} - 26 q^{49} - 16 q^{50} - 20 q^{51} + 24 q^{54} - 4 q^{56} - 4 q^{59} + 16 q^{60} + 20 q^{61} - 6 q^{64} + 4 q^{65} + 56 q^{69} + 12 q^{70} - 16 q^{71} + 16 q^{74} - 10 q^{75} + 4 q^{76} - 56 q^{79} - 2 q^{81} - 24 q^{84} + 28 q^{85} - 24 q^{86} + 4 q^{89} - 2 q^{90} - 4 q^{91} + 20 q^{94} - 4 q^{95} - 20 q^{99} + O(q^{100}) \)

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.b.a $6$ $1.038$ 6.0.3534400.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{3}-\beta _{4})q^{3}-q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)

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

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