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Properties

Label 130.2.j
Level 130
Weight 2
Character orbit j
Rep. character \(\chi_{130}(47,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 14
Newforms 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: \(\Q(i)\)
Newforms: \( 5 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(130, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
130.2.j.a \(2\) \(1.038\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(-8\) \(q-iq^{2}+(-2+2i)q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
130.2.j.b \(2\) \(1.038\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-4\) \(q+iq^{2}+(-1+i)q^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
130.2.j.c \(2\) \(1.038\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(-4\) \(q-iq^{2}+(1-i)q^{3}-q^{4}+(2-i)q^{5}+\cdots\)
130.2.j.d \(4\) \(1.038\) \(\Q(i, \sqrt{11})\) None \(0\) \(2\) \(0\) \(12\) \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}-q^{4}+\cdots\)
130.2.j.e \(4\) \(1.038\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(4\) \(4\) \(q-\zeta_{12}^{3}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)

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

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