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Properties

Label 260.2.m
Level $260$
Weight $2$
Character orbit 260.m
Rep. character $\chi_{260}(57,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $14$
Newform subspaces $3$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 96 14 82
Cusp forms 72 14 58
Eisenstein series 24 0 24

Trace form

\( 14 q + O(q^{10}) \) \( 14 q + 12 q^{15} + 2 q^{17} + 12 q^{19} - 12 q^{21} - 12 q^{23} - 14 q^{25} - 12 q^{27} + 52 q^{33} + 12 q^{35} - 12 q^{39} + 2 q^{41} - 12 q^{43} - 18 q^{45} - 14 q^{49} - 18 q^{53} - 28 q^{55} - 4 q^{57} - 16 q^{59} - 24 q^{63} + 30 q^{65} - 32 q^{67} + 40 q^{69} - 12 q^{71} - 32 q^{73} - 28 q^{75} + 40 q^{77} - 6 q^{81} - 14 q^{85} + 8 q^{87} + 18 q^{89} + 16 q^{91} - 36 q^{95} + 16 q^{97} - 20 q^{99} + O(q^{100}) \)

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.m.a 260.m 65.k $2$ $2.076$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{3}+(-1+2i)q^{5}-4iq^{7}+\cdots\)
260.2.m.b 260.m 65.k $4$ $2.076$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
260.2.m.c 260.m 65.k $8$ $2.076$ 8.0.\(\cdots\).2 None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(\beta _{3}-\beta _{6})q^{5}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)

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

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