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Properties

Label 130.2.d
Level $130$
Weight $2$
Character orbit 130.d
Rep. character $\chi_{130}(51,\cdot)$
Character field $\Q$
Dimension $2$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 2 24
Cusp forms 18 2 16
Eisenstein series 8 0 8

Trace form

\( 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9} - 2 q^{10} - 4 q^{12} + 4 q^{13} + 2 q^{16} - 12 q^{17} - 2 q^{25} + 6 q^{26} - 8 q^{27} + 12 q^{29} - 4 q^{30} - 2 q^{36} + 8 q^{39} + 2 q^{40} - 20 q^{43} + 4 q^{48} + 14 q^{49} - 24 q^{51} - 4 q^{52} + 20 q^{61} + 12 q^{62} - 2 q^{64} + 6 q^{65} + 12 q^{68} + 12 q^{74} - 4 q^{75} + 12 q^{78} - 16 q^{79} - 22 q^{81} + 24 q^{87} - 2 q^{90} - 24 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
130.2.d.a 130.d 13.b $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2q^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(130, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)