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Properties

Label 261.6.c
Level $261$
Weight $6$
Character orbit 261.c
Rep. character $\chi_{261}(28,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $4$
Sturm bound $180$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 261.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(261, [\chi])\).

Total New Old
Modular forms 154 64 90
Cusp forms 146 62 84
Eisenstein series 8 2 6

Trace form

\( 62 q - 972 q^{4} + 150 q^{5} + 172 q^{7} + O(q^{10}) \) \( 62 q - 972 q^{4} + 150 q^{5} + 172 q^{7} - 482 q^{13} + 14812 q^{16} - 3684 q^{20} + 4868 q^{22} - 360 q^{23} + 41252 q^{25} + 5820 q^{28} - 24 q^{29} + 31316 q^{34} + 28008 q^{35} + 24576 q^{38} + 121134 q^{49} + 83808 q^{52} + 3618 q^{53} + 124444 q^{58} - 17556 q^{59} - 85008 q^{62} - 192184 q^{64} + 89430 q^{65} - 18608 q^{67} + 191652 q^{71} - 299592 q^{74} + 169512 q^{80} - 231040 q^{82} - 17268 q^{83} - 119748 q^{86} - 345188 q^{88} - 123508 q^{91} + 192996 q^{92} - 359068 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(261, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
261.6.c.a 261.c 29.b $6$ $41.860$ 6.0.\(\cdots\).1 \(\Q(\sqrt{-87}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3\beta _{1}+\beta _{5})q^{2}+(-2^{5}+10\beta _{2}-13\beta _{4}+\cdots)q^{4}+\cdots\)
261.6.c.b 261.c 29.b $12$ $41.860$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-46\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-14+\beta _{2})q^{4}+(-4-\beta _{6}+\cdots)q^{5}+\cdots\)
261.6.c.c 261.c 29.b $20$ $41.860$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(272\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{11}q^{2}+(-11+\beta _{1})q^{4}+\beta _{12}q^{5}+\cdots\)
261.6.c.d 261.c 29.b $24$ $41.860$ None \(0\) \(0\) \(196\) \(-120\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(261, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)