Properties

Label 33.5.c
Level $33$
Weight $5$
Character orbit 33.c
Rep. character $\chi_{33}(10,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(33, [\chi])\).

Total New Old
Modular forms 18 8 10
Cusp forms 14 8 6
Eisenstein series 4 0 4

Trace form

\( 8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10}) \) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
33.5.c.a \(8\) \(3.411\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-36\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-10-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)