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Properties

Label 260.2.a
Level $260$
Weight $2$
Character orbit 260.a
Rep. character $\chi_{260}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(260))\).

Total New Old
Modular forms 48 4 44
Cusp forms 37 4 33
Eisenstein series 11 0 11

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
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(4\)

Trace form

\( 4 q + 4 q^{3} + 2 q^{5} + 12 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{3} + 2 q^{5} + 12 q^{9} + 4 q^{11} + 2 q^{13} + 4 q^{17} + 8 q^{19} - 4 q^{21} - 16 q^{23} + 4 q^{25} + 4 q^{27} - 12 q^{31} - 4 q^{33} - 4 q^{35} + 8 q^{37} - 4 q^{41} + 10 q^{45} - 16 q^{47} + 20 q^{49} - 32 q^{51} - 16 q^{53} - 4 q^{55} - 20 q^{57} - 24 q^{59} + 16 q^{61} - 48 q^{63} + 4 q^{65} + 8 q^{67} - 8 q^{71} + 24 q^{73} + 4 q^{75} - 28 q^{77} - 8 q^{79} + 12 q^{81} - 20 q^{87} + 8 q^{89} - 4 q^{91} - 20 q^{93} + 8 q^{95} + 28 q^{97} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(260))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 13
260.2.a.a 260.a 1.a $1$ $2.076$ \(\Q\) None \(0\) \(2\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
260.2.a.b 260.a 1.a $3$ $2.076$ 3.3.564.1 None \(0\) \(2\) \(3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(260))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(260)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 2}\)