Properties

Label 130.2.c
Level $130$
Weight $2$
Character orbit 130.c
Rep. character $\chi_{130}(129,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $42$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 130.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

Trace form

\( 8 q + 8 q^{4} - 4 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{4} - 4 q^{9} - 6 q^{10} - 4 q^{14} + 8 q^{16} + 2 q^{25} - 8 q^{26} - 24 q^{29} - 2 q^{30} - 30 q^{35} - 4 q^{36} - 24 q^{39} - 6 q^{40} + 12 q^{49} + 52 q^{51} + 40 q^{55} - 4 q^{56} - 8 q^{61} + 8 q^{64} + 6 q^{65} + 32 q^{66} + 88 q^{69} - 4 q^{74} - 30 q^{75} - 8 q^{79} - 16 q^{81} + 36 q^{90} + 4 q^{91} - 60 q^{94} - 36 q^{95} + O(q^{100}) \)

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.c.a 130.c 65.d $4$ $1.038$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots\)
130.2.c.b 130.c 65.d $4$ $1.038$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots\)

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

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