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Properties

Label 130.2.p
Level $130$
Weight $2$
Character orbit 130.p
Rep. character $\chi_{130}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $28$
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.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
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 100 28 72
Cusp forms 68 28 40
Eisenstein series 32 0 32

Trace form

\( 28 q + 14 q^{4} - 2 q^{5} - 24 q^{9} + O(q^{10}) \) \( 28 q + 14 q^{4} - 2 q^{5} - 24 q^{9} + 12 q^{11} - 10 q^{13} - 14 q^{16} - 4 q^{17} - 4 q^{18} + 36 q^{19} + 2 q^{20} - 24 q^{21} - 26 q^{25} - 24 q^{27} + 12 q^{30} - 24 q^{31} - 12 q^{33} - 26 q^{34} - 12 q^{35} - 24 q^{36} - 20 q^{37} - 26 q^{41} + 12 q^{42} + 12 q^{44} + 12 q^{45} - 12 q^{46} + 64 q^{47} - 2 q^{49} - 24 q^{50} + 4 q^{52} - 6 q^{53} + 40 q^{55} + 12 q^{56} + 14 q^{58} - 28 q^{59} + 24 q^{60} + 24 q^{61} + 24 q^{62} + 120 q^{63} - 28 q^{64} + 8 q^{65} + 16 q^{66} + 24 q^{67} - 2 q^{68} + 16 q^{69} - 8 q^{70} + 24 q^{71} - 2 q^{72} + 30 q^{74} + 32 q^{75} + 24 q^{76} + 88 q^{77} + 68 q^{78} + 4 q^{80} + 6 q^{81} - 62 q^{82} - 112 q^{83} + 22 q^{85} - 32 q^{87} - 18 q^{89} - 30 q^{90} + 32 q^{91} - 68 q^{93} + 24 q^{94} + 24 q^{95} - 108 q^{97} - 48 q^{98} + 28 q^{99} + O(q^{100}) \)

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.p.a 130.p 65.t $12$ $1.038$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{6}q^{2}+(\beta _{5}+\beta _{7}+\beta _{8}+\beta _{11})q^{3}+\cdots\)
130.2.p.b 130.p 65.t $16$ $1.038$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(1+\beta _{8}+\cdots)q^{4}+\cdots\)

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

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