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Properties

Label 260.2.ba
Level $260$
Weight $2$
Character orbit 260.ba
Rep. character $\chi_{260}(9,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(260, [\chi])\).

Total New Old
Modular forms 96 12 84
Cusp forms 72 12 60
Eisenstein series 24 0 24

Trace form

\( 12 q + 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{9} + 6 q^{11} + 10 q^{15} + 10 q^{19} + 12 q^{21} + 4 q^{25} - 10 q^{29} - 24 q^{31} - 6 q^{35} - 18 q^{39} + 2 q^{41} + 12 q^{45} - 4 q^{49} - 76 q^{51} - 2 q^{59} + 22 q^{61} - 40 q^{65} - 26 q^{69} - 14 q^{71} - 8 q^{75} + 8 q^{79} - 22 q^{81} + 14 q^{85} + 2 q^{89} + 58 q^{91} - 20 q^{95} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(260, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
260.2.ba.a 260.ba 65.n $12$ $2.076$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{10})q^{3}+(-\beta _{7}-\beta _{11})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)