Properties

Label 261.2.l
Level $261$
Weight $2$
Character orbit 261.l
Rep. character $\chi_{261}(41,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 261.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 261 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 128 128 0
Cusp forms 112 112 0
Eisenstein series 16 16 0

Trace form

\( 112 q - 6 q^{2} - 4 q^{3} - 4 q^{7} + O(q^{10}) \) \( 112 q - 6 q^{2} - 4 q^{3} - 4 q^{7} + 6 q^{11} - 18 q^{12} - 18 q^{14} - 8 q^{15} + 40 q^{16} + 22 q^{18} - 8 q^{19} - 12 q^{20} + 24 q^{21} - 12 q^{23} - 96 q^{24} - 44 q^{25} + 20 q^{27} - 42 q^{29} + 28 q^{30} - 2 q^{31} - 66 q^{32} + 12 q^{36} - 8 q^{37} - 12 q^{39} - 12 q^{40} - 18 q^{41} - 2 q^{43} - 52 q^{45} + 8 q^{46} - 36 q^{49} + 24 q^{50} - 36 q^{52} + 8 q^{54} + 36 q^{55} + 84 q^{56} + 28 q^{58} + 48 q^{59} - 36 q^{60} - 14 q^{61} + 24 q^{65} + 18 q^{66} - 102 q^{68} + 36 q^{69} - 8 q^{73} + 144 q^{74} + 18 q^{75} + 14 q^{76} - 72 q^{77} + 12 q^{78} - 2 q^{79} - 56 q^{81} + 80 q^{82} - 120 q^{83} - 14 q^{84} - 48 q^{85} - 76 q^{87} - 36 q^{88} + 160 q^{90} - 40 q^{94} + 204 q^{95} + 22 q^{97} - 54 q^{99} + O(q^{100}) \)

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.l.a 261.l 261.l $112$ $2.084$ None \(-6\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$