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Properties

Label 261.3.b
Level $261$
Weight $3$
Character orbit 261.b
Rep. character $\chi_{261}(233,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(261, [\chi])\).

Total New Old
Modular forms 64 20 44
Cusp forms 56 20 36
Eisenstein series 8 0 8

Trace form

\( 20 q - 40 q^{4} + 16 q^{7} + O(q^{10}) \) \( 20 q - 40 q^{4} + 16 q^{7} - 24 q^{10} - 24 q^{13} + 72 q^{16} + 40 q^{19} + 92 q^{22} - 76 q^{25} - 124 q^{28} - 56 q^{31} + 4 q^{34} - 80 q^{40} + 64 q^{43} + 120 q^{46} + 28 q^{49} + 452 q^{52} - 280 q^{55} - 16 q^{61} - 92 q^{64} - 88 q^{67} - 576 q^{70} + 320 q^{73} - 344 q^{76} + 328 q^{79} + 208 q^{82} + 328 q^{85} - 528 q^{88} + 248 q^{91} + 636 q^{94} - 464 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(261, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
261.3.b.a 261.b 3.b $20$ $7.112$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(261, [\chi]) \cong \)