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Properties

Label 260.2.c
Level $260$
Weight $2$
Character orbit 260.c
Rep. character $\chi_{260}(209,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 48 6 42
Cusp forms 36 6 30
Eisenstein series 12 0 12

Trace form

\( 6 q + 2 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{9} - 4 q^{15} - 4 q^{19} - 12 q^{21} + 2 q^{25} + 4 q^{29} + 12 q^{35} + 16 q^{41} - 12 q^{45} + 10 q^{49} - 8 q^{51} + 12 q^{55} - 4 q^{59} - 28 q^{61} - 2 q^{65} - 16 q^{69} + 20 q^{71} + 8 q^{75} - 8 q^{79} - 26 q^{81} - 20 q^{85} - 20 q^{89} + 8 q^{91} - 28 q^{95} + 28 q^{99} + O(q^{100}) \)

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.c.a 260.c 5.b $6$ $2.076$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-\beta _{1}-\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)

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

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