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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

\( 24 q + 4 q^{2} - 44 q^{4} + 16 q^{5} + 12 q^{6} + 52 q^{7} - 116 q^{8} - 54 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{2} - 44 q^{4} + 16 q^{5} + 12 q^{6} + 52 q^{7} - 116 q^{8} - 54 q^{9} - 112 q^{10} - 100 q^{11} + 24 q^{12} + 76 q^{13} + 418 q^{14} + 150 q^{15} + 368 q^{16} + 148 q^{17} - 54 q^{18} - 8 q^{19} - 354 q^{20} - 336 q^{21} - 674 q^{22} - 624 q^{23} - 126 q^{24} - 86 q^{25} - 478 q^{26} + 42 q^{28} + 820 q^{29} + 684 q^{30} + 230 q^{31} + 1416 q^{32} - 66 q^{33} + 1488 q^{34} + 240 q^{35} - 396 q^{36} + 108 q^{37} + 46 q^{38} + 336 q^{39} - 1282 q^{40} - 1460 q^{41} + 168 q^{42} - 360 q^{43} - 154 q^{44} + 144 q^{45} - 1766 q^{46} - 536 q^{47} + 336 q^{48} - 1794 q^{49} - 1578 q^{50} - 216 q^{51} + 1606 q^{52} + 1016 q^{53} - 432 q^{54} + 2940 q^{55} + 132 q^{56} - 1044 q^{57} + 50 q^{58} - 1060 q^{59} - 972 q^{60} + 1680 q^{61} - 272 q^{62} + 468 q^{63} - 208 q^{64} + 4240 q^{65} + 1296 q^{66} - 896 q^{67} + 3880 q^{68} + 540 q^{69} - 584 q^{70} + 1104 q^{71} + 1206 q^{72} + 866 q^{73} - 306 q^{74} + 1920 q^{75} - 6048 q^{76} - 724 q^{77} - 240 q^{78} + 84 q^{79} - 4078 q^{80} - 486 q^{81} + 1626 q^{82} - 7984 q^{83} - 1620 q^{84} - 2340 q^{85} - 5672 q^{86} - 6588 q^{87} + 1728 q^{88} - 3320 q^{89} - 828 q^{90} + 2500 q^{91} + 6782 q^{92} - 1788 q^{93} + 4406 q^{94} + 3768 q^{95} + 2334 q^{96} + 4008 q^{97} + 13640 q^{98} + 900 q^{99} + O(q^{100}) \)

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.e.a 33.e 11.c $4$ $1.947$ \(\Q(\zeta_{10})\) None \(10\) \(-3\) \(-21\) \(37\) $\mathrm{SU}(2)[C_{5}]$ \(q+(4-2\zeta_{10}+4\zeta_{10}^{2})q^{2}-3\zeta_{10}^{3}q^{3}+\cdots\)
33.4.e.b 33.e 11.c $8$ $1.947$ 8.0.682515625.5 None \(-6\) \(-6\) \(9\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-2\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
33.4.e.c 33.e 11.c $12$ $1.947$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(9\) \(28\) \(12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{7})q^{2}-3\beta _{6}q^{3}+\cdots\)

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

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