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Properties

Label 33.8.d
Level $33$
Weight $8$
Character orbit 33.d
Rep. character $\chi_{33}(32,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 33.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(33, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

Trace form

\( 26 q + 37 q^{3} + 1532 q^{4} - 3425 q^{9} + O(q^{10}) \) \( 26 q + 37 q^{3} + 1532 q^{4} - 3425 q^{9} + 3688 q^{12} + 13007 q^{15} + 38612 q^{16} - 17556 q^{22} + 10644 q^{25} - 19664 q^{27} + 209458 q^{31} + 218977 q^{33} - 436080 q^{34} - 624752 q^{36} - 52454 q^{37} - 100296 q^{42} - 1011553 q^{45} + 1812676 q^{48} + 477782 q^{49} - 2322914 q^{55} - 2920440 q^{58} + 3281036 q^{60} + 10384292 q^{64} + 2895156 q^{66} + 9098542 q^{67} - 1489129 q^{69} - 6924504 q^{70} - 6257742 q^{75} - 26237448 q^{78} + 19126627 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 22154513 q^{93} + 42583402 q^{97} + 37852441 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.8.d.a 33.d 33.d $2$ $10.309$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-83\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-35-13\beta )q^{3}-2^{7}q^{4}+(71-142\beta )q^{5}+\cdots\)
33.8.d.b 33.d 33.d $24$ $10.309$ None \(0\) \(120\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$