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Properties

Label 261.2.q
Level $261$
Weight $2$
Character orbit 261.q
Rep. character $\chi_{261}(7,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $336$
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.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 261 \)
Character field: \(\Q(\zeta_{21})\)
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 384 384 0
Cusp forms 336 336 0
Eisenstein series 48 48 0

Trace form

\( 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} + O(q^{10}) \) \( 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19} - 15 q^{20} - 2 q^{21} - 13 q^{22} - 32 q^{23} + 44 q^{24} + 15 q^{25} - 4 q^{26} - 43 q^{27} - 72 q^{28} - q^{29} - 8 q^{30} - 5 q^{31} + 7 q^{32} - 37 q^{33} - 15 q^{34} + 16 q^{35} - 104 q^{36} - 20 q^{37} + 63 q^{38} + 38 q^{39} + 5 q^{40} - 20 q^{41} + 11 q^{42} - 5 q^{43} - 8 q^{44} + 30 q^{45} - 80 q^{46} + 5 q^{47} + 12 q^{48} - 19 q^{49} - 3 q^{50} - 62 q^{51} + q^{52} - 4 q^{53} + 26 q^{54} - 100 q^{55} - 5 q^{56} - 50 q^{57} - 7 q^{58} + 154 q^{59} + 23 q^{60} + 7 q^{61} - 4 q^{62} - 144 q^{63} + 18 q^{64} - 65 q^{65} + 44 q^{66} - 5 q^{67} - 9 q^{68} + 22 q^{69} - 14 q^{70} + 18 q^{71} + 37 q^{72} - 20 q^{73} - 77 q^{74} + 16 q^{75} - 5 q^{76} + 39 q^{77} + 52 q^{78} - 5 q^{79} - 104 q^{80} + 54 q^{81} + 12 q^{82} - 23 q^{83} + 175 q^{84} - 42 q^{85} + 128 q^{86} + 42 q^{87} - 8 q^{88} + 34 q^{89} + 222 q^{90} + 12 q^{91} - 115 q^{92} + 64 q^{93} - 25 q^{94} + 89 q^{95} - 49 q^{96} + 55 q^{97} - 88 q^{98} + 196 q^{99} + O(q^{100}) \)

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.q.a 261.q 261.q $336$ $2.084$ None \(-5\) \(-10\) \(-9\) \(-5\) $\mathrm{SU}(2)[C_{21}]$