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Properties

Label 33.3.c
Level $33$
Weight $3$
Character orbit 33.c
Rep. character $\chi_{33}(10,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(33, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\( 4 q - 20 q^{4} + 4 q^{5} + 12 q^{9} + O(q^{10}) \) \( 4 q - 20 q^{4} + 4 q^{5} + 12 q^{9} + 20 q^{11} + 24 q^{12} + 12 q^{14} - 36 q^{15} + 4 q^{16} - 92 q^{20} - 12 q^{22} - 92 q^{23} + 12 q^{25} + 204 q^{26} + 80 q^{31} - 12 q^{33} + 48 q^{34} - 60 q^{36} - 64 q^{37} - 120 q^{38} + 84 q^{42} - 124 q^{44} + 12 q^{45} + 100 q^{47} - 144 q^{48} + 100 q^{49} + 28 q^{53} + 56 q^{55} + 156 q^{56} - 240 q^{58} + 40 q^{59} + 204 q^{60} + 28 q^{64} + 192 q^{66} - 136 q^{67} - 60 q^{69} - 240 q^{70} - 284 q^{71} - 72 q^{75} - 180 q^{77} - 228 q^{78} + 436 q^{80} + 36 q^{81} + 216 q^{82} - 216 q^{86} + 396 q^{88} + 304 q^{89} + 24 q^{91} + 340 q^{92} + 216 q^{93} - 376 q^{97} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.3.c.a 33.c 11.b $4$ $0.899$ 4.0.39744.5 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-5-2\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)