Properties

Label 130.2.a
Level $130$
Weight $2$
Character orbit 130.a
Rep. character $\chi_{130}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $42$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 130.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(42\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(130))\).

Total New Old
Modular forms 24 3 21
Cusp forms 17 3 14
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(13\)FrickeDim.
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3 q + q^{2} + 3 q^{4} + q^{5} + 4 q^{6} - 8 q^{7} + q^{8} - q^{9} + O(q^{10}) \) \( 3 q + q^{2} + 3 q^{4} + q^{5} + 4 q^{6} - 8 q^{7} + q^{8} - q^{9} - q^{10} - 8 q^{11} + q^{13} - 4 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} + q^{20} + 4 q^{22} + 8 q^{23} + 4 q^{24} + 3 q^{25} - q^{26} - 8 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} + 8 q^{33} + 10 q^{34} - q^{36} + 6 q^{37} - 4 q^{38} - 4 q^{39} - q^{40} + 14 q^{41} - 16 q^{42} - 8 q^{43} - 8 q^{44} - 3 q^{45} - 4 q^{46} - 16 q^{47} + 11 q^{49} + q^{50} + 16 q^{51} + q^{52} + 14 q^{53} - 8 q^{54} - 4 q^{55} + 8 q^{57} + 6 q^{58} + 24 q^{59} - 4 q^{60} + 2 q^{61} - 12 q^{62} - 8 q^{63} + 3 q^{64} + 3 q^{65} - 16 q^{66} - 12 q^{67} - 2 q^{68} + 8 q^{70} - 8 q^{71} - 3 q^{72} + 10 q^{73} + 2 q^{74} + 32 q^{77} - 16 q^{79} + q^{80} - 13 q^{81} + 26 q^{82} + 12 q^{83} - 6 q^{85} - 12 q^{86} + 16 q^{87} + 4 q^{88} - 10 q^{89} - 5 q^{90} + 8 q^{92} - 16 q^{93} + 8 q^{94} - 12 q^{95} + 4 q^{96} + 2 q^{97} - 7 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(130))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 13
130.2.a.a $1$ $1.038$ \(\Q\) None \(-1\) \(-2\) \(1\) \(-4\) $+$ $-$ $-$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-4q^{7}+\cdots\)
130.2.a.b $1$ $1.038$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
130.2.a.c $1$ $1.038$ \(\Q\) None \(1\) \(2\) \(-1\) \(-4\) $-$ $+$ $+$ \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(130))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(130)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)