Properties

Label 891.2.f
Level $891$
Weight $2$
Character orbit 891.f
Rep. character $\chi_{891}(82,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $176$
Newform subspaces $7$
Sturm bound $216$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 7 \)
Sturm bound: \(216\)
Trace bound: \(2\)
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

\( 176 q - 34 q^{4} + 6 q^{7} - 40 q^{10} + 6 q^{13} - 10 q^{16} + 6 q^{19} + 22 q^{22} - 28 q^{25} - 72 q^{28} - 4 q^{34} - 18 q^{37} + 26 q^{40} + 28 q^{43} + 24 q^{46} - 50 q^{49} + 30 q^{52} - 26 q^{55}+ \cdots + 18 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
891.2.f.a 891.f 11.c $4$ $7.115$ \(\Q(\zeta_{10})\) None 99.2.m.a \(-4\) \(0\) \(6\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
891.2.f.b 891.f 11.c $4$ $7.115$ \(\Q(\zeta_{10})\) None 99.2.m.a \(4\) \(0\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots\)
891.2.f.c 891.f 11.c $24$ $7.115$ None 891.2.f.c \(-2\) \(0\) \(4\) \(7\) $\mathrm{SU}(2)[C_{5}]$
891.2.f.d 891.f 11.c $24$ $7.115$ None 891.2.f.c \(2\) \(0\) \(-4\) \(7\) $\mathrm{SU}(2)[C_{5}]$
891.2.f.e 891.f 11.c $36$ $7.115$ None 99.2.m.b \(-1\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{5}]$
891.2.f.f 891.f 11.c $36$ $7.115$ None 99.2.m.b \(1\) \(0\) \(8\) \(2\) $\mathrm{SU}(2)[C_{5}]$
891.2.f.g 891.f 11.c $48$ $7.115$ None 891.2.f.g \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(891, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)