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Properties

Label 891.2.u
Level $891$
Weight $2$
Character orbit 891.u
Rep. character $\chi_{891}(107,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $368$
Newform subspaces $6$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.u (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 6 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 960 400 560
Cusp forms 768 368 400
Eisenstein series 192 32 160

Trace form

\( 368 q + 50 q^{4} + 10 q^{7} + O(q^{10}) \) \( 368 q + 50 q^{4} + 10 q^{7} + 10 q^{13} + 38 q^{16} + 40 q^{19} + 10 q^{22} - 38 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 24 q^{37} - 30 q^{40} + 20 q^{46} - 28 q^{49} + 10 q^{52} + 24 q^{55} + 88 q^{58} + 10 q^{61} - 68 q^{64} - 20 q^{67} + 36 q^{70} - 20 q^{73} + 10 q^{79} - 32 q^{82} + 10 q^{85} + 238 q^{88} - 140 q^{91} + 10 q^{94} - 54 q^{97} + O(q^{100}) \)

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.u.a 891.u 99.p $16$ $7.115$ \(\Q(\zeta_{60})\) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{30}]$ \(q+(\zeta_{60}^{5}+\zeta_{60}^{11})q^{2}+(-\zeta_{60}^{2}+\zeta_{60}^{10}+\cdots)q^{4}+\cdots\)
891.2.u.b 891.u 99.p $32$ $7.115$ None \(0\) \(0\) \(-15\) \(0\) $\mathrm{SU}(2)[C_{30}]$
891.2.u.c 891.u 99.p $32$ $7.115$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$
891.2.u.d 891.u 99.p $32$ $7.115$ None \(0\) \(0\) \(15\) \(0\) $\mathrm{SU}(2)[C_{30}]$
891.2.u.e 891.u 99.p $64$ $7.115$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$
891.2.u.f 891.u 99.p $192$ $7.115$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

\( S_{2}^{\mathrm{old}}(891, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)