↑

Properties

Label 260.2.bk
Level $260$
Weight $2$
Character orbit 260.bk
Rep. character $\chi_{260}(33,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $28$
Newform subspaces $3$
Sturm bound $84$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(84\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 192 28 164
Cusp forms 144 28 116
Eisenstein series 48 0 48

Trace form

\( 28 q - 12 q^{9} + O(q^{10}) \) \( 28 q - 12 q^{9} + 12 q^{13} - 12 q^{15} - 2 q^{17} + 12 q^{19} + 12 q^{21} - 12 q^{23} + 2 q^{25} - 24 q^{27} + 24 q^{31} - 4 q^{33} - 12 q^{35} - 18 q^{37} + 12 q^{39} + 22 q^{41} - 12 q^{45} + 26 q^{49} + 6 q^{53} + 4 q^{55} - 56 q^{57} - 8 q^{59} - 12 q^{61} - 12 q^{63} - 30 q^{65} + 32 q^{67} - 16 q^{69} - 100 q^{73} - 44 q^{75} + 8 q^{77} - 6 q^{81} + 26 q^{85} + 4 q^{87} - 30 q^{89} - 16 q^{91} - 36 q^{93} - 12 q^{95} + 56 q^{97} + 56 q^{99} + O(q^{100}) \)

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.bk.a 260.bk 65.o $4$ $2.076$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-8\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-2+\zeta_{12}^{3})q^{5}+\cdots\)
260.2.bk.b 260.bk 65.o $4$ $2.076$ \(\Q(\zeta_{12})\) None \(0\) \(4\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12})q^{3}+(-1-2\zeta_{12}^{3})q^{5}+\cdots\)
260.2.bk.c 260.bk 65.o $20$ $2.076$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-2\) \(12\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+2\beta _{7}+\cdots)q^{3}+\cdots\)

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

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