Properties

Label 130.2.l
Level $130$
Weight $2$
Character orbit 130.l
Rep. character $\chi_{130}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
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.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
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 52 12 40
Cusp forms 36 12 24
Eisenstein series 16 0 16

Trace form

\( 12q + 6q^{4} - 6q^{9} + O(q^{10}) \) \( 12q + 6q^{4} - 6q^{9} + 2q^{10} - 6q^{11} + 12q^{13} - 12q^{14} + 12q^{15} - 6q^{16} - 18q^{19} - 12q^{25} + 24q^{27} + 12q^{29} + 4q^{30} - 60q^{33} - 6q^{35} + 6q^{36} - 12q^{37} - 24q^{38} - 36q^{39} + 4q^{40} - 24q^{41} - 12q^{42} + 12q^{46} + 12q^{49} + 24q^{51} + 48q^{53} + 36q^{54} + 12q^{55} - 6q^{56} + 12q^{58} + 12q^{59} + 24q^{61} + 24q^{62} + 48q^{63} - 12q^{64} + 6q^{65} - 24q^{66} + 24q^{67} + 12q^{69} + 24q^{72} + 18q^{74} - 18q^{76} - 24q^{77} + 12q^{78} + 24q^{79} - 30q^{81} + 12q^{84} - 36q^{85} + 24q^{87} - 42q^{89} - 4q^{90} - 66q^{91} + 36q^{93} + 6q^{94} + 36q^{97} - 48q^{98} + O(q^{100}) \)

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.l.a \(4\) \(1.038\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
130.2.l.b \(8\) \(1.038\) 8.0.22581504.2 None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)