Properties

Label 33.4.f
Level $33$
Weight $4$
Character orbit 33.f
Rep. character $\chi_{33}(2,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $40$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 33.f (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(33, [\chi])\).

Total New Old
Modular forms 56 56 0
Cusp forms 40 40 0
Eisenstein series 16 16 0

Trace form

\( 40 q - 3 q^{3} - 38 q^{4} + 45 q^{6} - 10 q^{7} - 65 q^{9} + O(q^{10}) \) \( 40 q - 3 q^{3} - 38 q^{4} + 45 q^{6} - 10 q^{7} - 65 q^{9} - 90 q^{12} - 10 q^{13} + 33 q^{15} + 310 q^{16} + 225 q^{18} - 460 q^{19} - 340 q^{22} - 565 q^{24} - 604 q^{25} - 435 q^{27} + 1190 q^{28} + 910 q^{30} + 840 q^{31} + 1208 q^{33} - 188 q^{34} + 1991 q^{36} + 126 q^{37} - 1075 q^{39} - 90 q^{40} - 3340 q^{42} - 1662 q^{45} + 430 q^{46} - 346 q^{48} + 376 q^{49} - 210 q^{51} - 4270 q^{52} - 546 q^{55} + 1800 q^{57} - 4582 q^{58} + 674 q^{60} + 650 q^{61} + 3945 q^{63} + 7238 q^{64} + 3504 q^{66} + 4556 q^{67} + 3860 q^{69} + 2964 q^{70} - 1640 q^{72} + 3860 q^{73} - 6048 q^{75} - 7640 q^{78} - 3550 q^{79} - 2453 q^{81} - 5812 q^{82} - 7080 q^{84} - 8230 q^{85} - 9298 q^{88} + 9220 q^{90} - 6766 q^{91} + 5659 q^{93} + 3530 q^{94} + 14890 q^{96} + 8004 q^{97} + 955 q^{99} + O(q^{100}) \)

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.f.a 33.f 33.f $40$ $1.947$ None \(0\) \(-3\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$