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Properties

Label 260.2.u
Level $260$
Weight $2$
Character orbit 260.u
Rep. character $\chi_{260}(99,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(i)\)
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 92 92 0
Cusp forms 76 76 0
Eisenstein series 16 16 0

Trace form

\( 76 q - 2 q^{5} - 12 q^{6} + 44 q^{9} + O(q^{10}) \) \( 76 q - 2 q^{5} - 12 q^{6} + 44 q^{9} + 8 q^{14} + 8 q^{16} - 4 q^{20} - 32 q^{21} - 32 q^{24} - 20 q^{26} - 16 q^{29} - 20 q^{34} + 28 q^{40} - 36 q^{41} - 12 q^{44} - 26 q^{45} + 44 q^{46} - 8 q^{50} - 116 q^{54} - 48 q^{60} - 56 q^{61} + 6 q^{65} - 16 q^{66} - 28 q^{70} - 8 q^{74} + 16 q^{76} - 68 q^{80} - 52 q^{81} - 12 q^{84} - 32 q^{85} + 16 q^{86} + 52 q^{89} + 88 q^{94} + 4 q^{96} + O(q^{100}) \)

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.u.a 260.u 260.u $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-2+i)q^{5}+\cdots\)
260.2.u.b 260.u 260.u $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(1-2i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
260.2.u.c 260.u 260.u $72$ $2.076$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$