Properties

Label 260.2.bg
Level $260$
Weight $2$
Character orbit 260.bg
Rep. character $\chi_{260}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $152$
Newform subspaces $3$
Sturm bound $84$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(84\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(17\)

Dimensions

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

Total New Old
Modular forms 184 184 0
Cusp forms 152 152 0
Eisenstein series 32 32 0

Trace form

\( 152 q - 6 q^{2} - 12 q^{6} + O(q^{10}) \) \( 152 q - 6 q^{2} - 12 q^{6} + 6 q^{10} - 12 q^{12} - 6 q^{13} + 4 q^{16} - 14 q^{17} - 30 q^{20} - 12 q^{22} - 36 q^{25} - 32 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 52 q^{36} + 18 q^{37} - 16 q^{38} + 68 q^{40} - 24 q^{41} + 40 q^{42} - 102 q^{45} - 12 q^{46} - 40 q^{48} + 78 q^{50} - 50 q^{52} - 12 q^{53} - 20 q^{56} + 66 q^{58} - 8 q^{61} - 44 q^{62} - 12 q^{65} + 96 q^{66} - 44 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} + 24 q^{80} + 4 q^{81} - 58 q^{82} - 12 q^{85} - 10 q^{88} - 20 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98} + O(q^{100}) \)

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.bg.a 260.bg 260.ag $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots\)
260.2.bg.b 260.bg 260.ag $4$ $2.076$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots\)
260.2.bg.c 260.bg 260.ag $144$ $2.076$ None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$