Properties

Label 260.2.i
Level $260$
Weight $2$
Character orbit 260.i
Rep. character $\chi_{260}(61,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $4$
Sturm bound $84$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(84\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

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

Total New Old
Modular forms 96 8 88
Cusp forms 72 8 64
Eisenstein series 24 0 24

Trace form

\( 8 q + 2 q^{3} - 6 q^{7} + O(q^{10}) \) \( 8 q + 2 q^{3} - 6 q^{7} - 4 q^{11} + 4 q^{13} + 2 q^{15} + 14 q^{17} + 4 q^{19} - 32 q^{21} - 2 q^{23} + 8 q^{25} - 28 q^{27} + 12 q^{29} - 2 q^{33} + 2 q^{35} + 10 q^{37} + 12 q^{39} + 4 q^{41} - 6 q^{43} - 8 q^{45} + 40 q^{47} - 8 q^{49} + 32 q^{51} - 8 q^{53} - 8 q^{55} - 4 q^{57} + 8 q^{61} - 12 q^{63} + 4 q^{65} - 14 q^{67} - 24 q^{69} - 16 q^{71} - 24 q^{73} + 2 q^{75} - 44 q^{77} + 8 q^{79} - 12 q^{81} + 24 q^{83} + 6 q^{85} - 10 q^{87} - 32 q^{89} - 8 q^{91} - 16 q^{93} + 8 q^{95} - 10 q^{97} + 32 q^{99} + O(q^{100}) \)

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.i.a 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
260.2.i.b 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
260.2.i.c 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
260.2.i.d 260.i 13.c $2$ $2.076$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)