Properties

Label 130.2.j
Level $130$
Weight $2$
Character orbit 130.j
Rep. character $\chi_{130}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $14$
Newform subspaces $5$
Sturm bound $42$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 130.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(42\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 50 14 36
Cusp forms 34 14 20
Eisenstein series 16 0 16

Trace form

\( 14 q - 14 q^{4} + 2 q^{5} + O(q^{10}) \) \( 14 q - 14 q^{4} + 2 q^{5} - 12 q^{11} - 14 q^{13} + 14 q^{16} - 2 q^{17} - 26 q^{18} + 12 q^{19} - 2 q^{20} + 24 q^{21} + 24 q^{23} + 2 q^{25} - 12 q^{27} + 24 q^{30} - 24 q^{31} + 2 q^{34} + 12 q^{35} + 32 q^{37} - 22 q^{41} - 12 q^{42} - 24 q^{43} + 12 q^{44} - 12 q^{45} - 12 q^{46} - 64 q^{47} - 10 q^{49} + 14 q^{52} + 30 q^{53} + 8 q^{55} + 28 q^{58} - 20 q^{59} + 12 q^{62} - 14 q^{64} + 10 q^{65} + 32 q^{66} + 2 q^{68} + 32 q^{69} + 44 q^{70} + 26 q^{72} - 56 q^{75} - 12 q^{76} + 8 q^{77} - 32 q^{78} + 2 q^{80} + 18 q^{81} - 34 q^{82} - 8 q^{83} - 24 q^{84} + 2 q^{85} - 16 q^{87} - 6 q^{89} + 30 q^{90} - 32 q^{91} - 24 q^{92} + 32 q^{93} + 24 q^{95} + 44 q^{99} + O(q^{100}) \)

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.j.a 130.j 65.f $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(-2+2i)q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
130.2.j.b 130.j 65.f $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(-1+i)q^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
130.2.j.c 130.j 65.f $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(1-i)q^{3}-q^{4}+(2-i)q^{5}+\cdots\)
130.2.j.d 130.j 65.f $4$ $1.038$ \(\Q(i, \sqrt{11})\) None \(0\) \(2\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}-q^{4}+\cdots\)
130.2.j.e 130.j 65.f $4$ $1.038$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{3}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)

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

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