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Properties

Label 130.4.n
Level $130$
Weight $4$
Character orbit 130.n
Rep. character $\chi_{130}(9,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(130, [\chi])\).

Total New Old
Modular forms 132 44 88
Cusp forms 116 44 72
Eisenstein series 16 0 16

Trace form

\( 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(130, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
130.4.n.a 130.n 65.n $44$ $7.670$ None 130.4.n.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(130, [\chi])\) into lower level spaces

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