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Properties

Label 891.2.k
Level $891$
Weight $2$
Character orbit 891.k
Rep. character $\chi_{891}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $176$
Newform subspaces $2$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(891, [\chi])\).

Total New Old
Modular forms 480 208 272
Cusp forms 384 176 208
Eisenstein series 96 32 64

Trace form

\( 176 q - 34 q^{4} + 10 q^{7} + O(q^{10}) \) \( 176 q - 34 q^{4} + 10 q^{7} + 10 q^{13} - 58 q^{16} - 50 q^{19} + 34 q^{22} + 28 q^{25} + 40 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 62 q^{49} + 10 q^{52} + 18 q^{55} - 38 q^{58} + 10 q^{61} - 80 q^{64} + 28 q^{67} - 108 q^{70} - 20 q^{73} + 130 q^{79} - 2 q^{82} - 50 q^{85} - 182 q^{88} + 100 q^{91} - 110 q^{94} - 90 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(891, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
891.2.k.a 891.k 33.f $80$ $7.115$ None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$
891.2.k.b 891.k 33.f $96$ $7.115$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(891, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(891, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)