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Properties

Label 261.2.c
Level $261$
Weight $2$
Character orbit 261.c
Rep. character $\chi_{261}(28,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
Sturm bound $60$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 34 14 20
Cusp forms 26 12 14
Eisenstein series 8 2 6

Trace form

\( 12 q - 16 q^{4} + 2 q^{5} - 4 q^{7} + O(q^{10}) \) \( 12 q - 16 q^{4} + 2 q^{5} - 4 q^{7} - 6 q^{13} + 16 q^{16} - 10 q^{20} - 6 q^{22} - 8 q^{23} - 18 q^{25} + 24 q^{28} + 6 q^{29} - 28 q^{34} + 40 q^{35} - 32 q^{38} + 44 q^{49} + 70 q^{52} - 18 q^{53} - 14 q^{58} - 12 q^{59} + 50 q^{62} - 108 q^{64} - 2 q^{65} + 8 q^{67} - 28 q^{71} - 4 q^{74} + 30 q^{80} + 36 q^{83} - 18 q^{86} + 42 q^{88} - 20 q^{91} + 48 q^{92} + 66 q^{94} + O(q^{100}) \)

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.c.a 261.c 29.b $2$ $2.084$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(6\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-3q^{4}+3q^{5}+2q^{7}-\beta q^{8}+\cdots\)
261.2.c.b 261.c 29.b $4$ $2.084$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+2\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
261.2.c.c 261.c 29.b $6$ $2.084$ 6.0.\(\cdots\).1 \(\Q(\sqrt{-87}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)

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

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