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Properties

Label 33.3.h
Level $33$
Weight $3$
Character orbit 33.h
Rep. character $\chi_{33}(5,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

Trace form

\( 24 q - 6 q^{3} + 2 q^{4} - 23 q^{6} + 2 q^{7} - 26 q^{9} + O(q^{10}) \) \( 24 q - 6 q^{3} + 2 q^{4} - 23 q^{6} + 2 q^{7} - 26 q^{9} - 56 q^{10} + 58 q^{12} - 10 q^{13} + 32 q^{15} - 98 q^{16} - 3 q^{18} - 22 q^{19} + 76 q^{21} + 20 q^{22} + 111 q^{24} + 92 q^{25} + 36 q^{27} + 342 q^{28} - 132 q^{30} + 106 q^{31} - 169 q^{33} - 84 q^{34} - 213 q^{36} - 30 q^{37} - 238 q^{39} - 242 q^{40} - 172 q^{42} - 420 q^{43} + 8 q^{45} + 2 q^{46} + 50 q^{48} - 180 q^{49} + 171 q^{51} + 362 q^{52} + 1046 q^{54} + 144 q^{55} + 417 q^{57} + 70 q^{58} + 234 q^{60} + 210 q^{61} - 134 q^{63} + 262 q^{64} - 360 q^{66} + 344 q^{67} - 42 q^{69} - 280 q^{70} - 842 q^{72} - 158 q^{73} - 157 q^{75} - 1164 q^{76} - 452 q^{78} - 774 q^{79} - 230 q^{81} - 72 q^{82} + 294 q^{84} + 282 q^{85} + 792 q^{87} + 798 q^{88} + 160 q^{90} + 458 q^{91} + 26 q^{93} + 1042 q^{94} - 662 q^{96} + 588 q^{97} - 490 q^{99} + O(q^{100}) \)

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.h.a 33.h 33.h $8$ $0.899$ \(\Q(\zeta_{20})\) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{2}+(2+2\zeta_{20}-2\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
33.3.h.b 33.h 33.h $16$ $0.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-10\) \(0\) \(6\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)