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Properties

Label 33.4.d
Level $33$
Weight $4$
Character orbit 33.d
Rep. character $\chi_{33}(32,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(33, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10 q - 2 q^{3} + 28 q^{4} - 20 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{3} + 28 q^{4} - 20 q^{9} - 80 q^{12} + 62 q^{15} - 140 q^{16} - 300 q^{22} + 174 q^{25} + 460 q^{27} + 140 q^{31} + 592 q^{33} + 768 q^{34} - 776 q^{36} - 16 q^{37} - 120 q^{42} - 1018 q^{45} - 1244 q^{48} - 1346 q^{49} - 1444 q^{55} + 1992 q^{58} + 3476 q^{60} - 2108 q^{64} + 2076 q^{66} + 1004 q^{67} - 2110 q^{69} + 5016 q^{70} + 2208 q^{75} + 120 q^{78} - 5372 q^{81} - 6408 q^{82} - 3852 q^{88} + 4776 q^{91} + 3866 q^{93} - 3904 q^{97} + 3010 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.4.d.a 33.d 33.d $2$ $1.947$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-8\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-4-\beta )q^{3}-8q^{4}-4\beta q^{5}+(5+8\beta )q^{9}+\cdots\)
33.4.d.b 33.d 33.d $8$ $1.947$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(1-\beta _{3})q^{3}+(5+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)