# 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 $1$

# Related objects

## 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

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

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

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

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

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