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Properties

Label 261.2.k
Level $261$
Weight $2$
Character orbit 261.k
Rep. character $\chi_{261}(82,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $66$
Newform subspaces $4$
Sturm bound $60$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 261.k (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(261, [\chi])\).

Total New Old
Modular forms 204 78 126
Cusp forms 156 66 90
Eisenstein series 48 12 36

Trace form

\( 66 q + 8 q^{2} - 12 q^{4} + 7 q^{5} - 7 q^{7} + 25 q^{8} + O(q^{10}) \) \( 66 q + 8 q^{2} - 12 q^{4} + 7 q^{5} - 7 q^{7} + 25 q^{8} - 3 q^{10} - 9 q^{11} + 11 q^{13} + 3 q^{14} - 14 q^{16} + 20 q^{17} - 7 q^{19} - 52 q^{20} - 22 q^{22} + 21 q^{23} + 14 q^{25} - 6 q^{26} - 4 q^{28} - 4 q^{29} - 27 q^{31} - 51 q^{32} - 64 q^{34} - 39 q^{35} - 25 q^{37} + 50 q^{38} - 12 q^{40} + 24 q^{41} + 9 q^{43} + 42 q^{44} - 16 q^{46} - 35 q^{47} - 16 q^{49} - 17 q^{50} + 14 q^{52} - 7 q^{53} - 21 q^{55} - 45 q^{56} + 62 q^{58} + 68 q^{59} + 63 q^{61} - 151 q^{62} - 77 q^{64} - 33 q^{65} - 13 q^{67} - 18 q^{68} + 134 q^{70} - 39 q^{71} - 59 q^{73} + 88 q^{74} + 95 q^{76} - q^{77} - 5 q^{79} + 178 q^{80} + 18 q^{82} - 9 q^{83} + 52 q^{85} + 40 q^{86} + 18 q^{88} + 71 q^{89} + 25 q^{91} + 110 q^{92} - 44 q^{94} + 75 q^{95} - 97 q^{97} - 39 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(261, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
261.2.k.a 261.k 29.d $6$ $2.084$ \(\Q(\zeta_{14})\) None \(2\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots\)
261.2.k.b 261.k 29.d $18$ $2.084$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(7\) \(-4\) $\mathrm{SU}(2)[C_{7}]$ \(q+\beta _{3}q^{2}+(-\beta _{10}-\beta _{16})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
261.2.k.c 261.k 29.d $18$ $2.084$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(4\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{7}]$ \(q+(\beta _{3}-\beta _{9})q^{2}+(2\beta _{1}+\beta _{5}-\beta _{6}+2\beta _{12}+\cdots)q^{4}+\cdots\)
261.2.k.d 261.k 29.d $24$ $2.084$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(261, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)