Properties

Label 33.4.e
Level $33$
Weight $4$
Character orbit 33.e
Rep. character $\chi_{33}(4,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $24$
Newform subspaces $3$
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.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
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 56 24 32
Cusp forms 40 24 16
Eisenstein series 16 0 16

Trace form

\( 24 q + 4 q^{2} - 44 q^{4} + 16 q^{5} + 12 q^{6} + 52 q^{7} - 116 q^{8} - 54 q^{9} - 112 q^{10} - 100 q^{11} + 24 q^{12} + 76 q^{13} + 418 q^{14} + 150 q^{15} + 368 q^{16} + 148 q^{17} - 54 q^{18} - 8 q^{19}+ \cdots + 900 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.4.e.a 33.e 11.c $4$ $1.947$ \(\Q(\zeta_{10})\) None 33.4.e.a \(10\) \(-3\) \(-21\) \(37\) $\mathrm{SU}(2)[C_{5}]$ \(q+(4-2\zeta_{10}+4\zeta_{10}^{2})q^{2}-3\zeta_{10}^{3}q^{3}+\cdots\)
33.4.e.b 33.e 11.c $8$ $1.947$ 8.0.682515625.5 None 33.4.e.b \(-6\) \(-6\) \(9\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-2\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
33.4.e.c 33.e 11.c $12$ $1.947$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 33.4.e.c \(0\) \(9\) \(28\) \(12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{7})q^{2}-3\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(33, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)