Properties

Label 260.2.p
Level $260$
Weight $2$
Character orbit 260.p
Rep. character $\chi_{260}(103,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $4$
Sturm bound $84$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(84\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(7\), \(37\)

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

\( 76 q + O(q^{10}) \) \( 76 q - 12 q^{10} - 24 q^{12} - 6 q^{13} + 8 q^{16} - 28 q^{17} - 24 q^{22} + 12 q^{25} + 20 q^{26} + 24 q^{30} - 8 q^{36} + 4 q^{38} - 56 q^{40} + 8 q^{42} - 44 q^{48} + 44 q^{52} - 12 q^{53} + 8 q^{56} - 16 q^{61} - 28 q^{62} - 30 q^{65} - 24 q^{66} - 40 q^{68} - 64 q^{77} - 20 q^{78} - 28 q^{81} + 52 q^{82} - 116 q^{88} + 8 q^{90} - 4 q^{92} + O(q^{100}) \)

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.p.a 260.p 260.p $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(2+i)q^{5}+\cdots\)
260.2.p.b 260.p 260.p $2$ $2.076$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(-2-i)q^{5}+\cdots\)
260.2.p.c 260.p 260.p $8$ $2.076$ 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
260.2.p.d 260.p 260.p $64$ $2.076$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$