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Properties

Label 130.2.s
Level $130$
Weight $2$
Character orbit 130.s
Rep. character $\chi_{130}(33,\cdot)$
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.s (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

\( 28 q + 2 q^{2} - 14 q^{4} - 4 q^{8} + 24 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{2} - 14 q^{4} - 4 q^{8} + 24 q^{9} + 12 q^{11} - 12 q^{13} - 14 q^{16} - 2 q^{17} - 36 q^{19} - 24 q^{21} + 26 q^{25} - 24 q^{27} - 12 q^{30} - 24 q^{31} + 2 q^{32} + 44 q^{33} + 26 q^{34} - 12 q^{35} - 24 q^{36} - 18 q^{37} - 26 q^{41} + 12 q^{42} - 12 q^{44} - 72 q^{45} - 12 q^{46} + 2 q^{49} + 28 q^{50} - 6 q^{53} - 32 q^{55} + 12 q^{56} + 64 q^{57} + 12 q^{58} + 28 q^{59} + 24 q^{60} + 24 q^{61} + 48 q^{62} + 28 q^{64} + 66 q^{65} + 16 q^{66} + 56 q^{67} + 4 q^{68} - 16 q^{69} + 24 q^{70} + 24 q^{71} + 24 q^{72} - 28 q^{73} - 30 q^{74} + 88 q^{75} + 24 q^{76} - 88 q^{77} + 36 q^{78} + 6 q^{81} - 28 q^{82} - 58 q^{85} - 80 q^{87} + 18 q^{89} + 30 q^{90} + 32 q^{91} - 36 q^{93} - 24 q^{94} - 24 q^{95} + 20 q^{97} - 2 q^{98} - 28 q^{99} + O(q^{100}) \)

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

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

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