Properties

Label 33.14
Level 33
Weight 14
Dimension 374
Nonzero newspaces 4
Sturm bound 1120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 33 = 3 \cdot 11 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(33))\).

Total New Old
Modular forms 540 394 146
Cusp forms 500 374 126
Eisenstein series 40 20 20

Trace form

\( 374 q + 132 q^{2} - 1463 q^{3} - 24946 q^{4} - 21012 q^{5} + 460911 q^{6} - 402960 q^{7} + 3579184 q^{8} - 6258721 q^{9} + O(q^{10}) \) \( 374 q + 132 q^{2} - 1463 q^{3} - 24946 q^{4} - 21012 q^{5} + 460911 q^{6} - 402960 q^{7} + 3579184 q^{8} - 6258721 q^{9} + 12400472 q^{10} + 3589310 q^{11} - 90716402 q^{12} - 10747956 q^{13} + 125494254 q^{14} - 155729653 q^{15} - 820770562 q^{16} + 967913106 q^{17} - 423381483 q^{18} - 1521827308 q^{19} - 464350358 q^{20} + 2088710388 q^{21} + 2422140386 q^{22} - 6155588780 q^{23} - 5399588359 q^{24} + 9020152068 q^{25} + 11239486198 q^{26} - 7210646318 q^{27} - 41125973600 q^{28} + 9979759984 q^{29} + 37290491758 q^{30} - 14613866198 q^{31} + 26034512020 q^{32} - 6726613359 q^{33} + 40103173388 q^{34} - 50809563160 q^{35} - 15565002021 q^{36} + 63813926970 q^{37} + 62447658118 q^{38} - 89319212320 q^{39} - 232079908436 q^{40} - 151275146448 q^{41} + 122024191100 q^{42} + 477867261732 q^{43} + 162163227358 q^{44} - 146985179257 q^{45} - 490872590088 q^{46} + 146266121654 q^{47} + 624154194258 q^{48} + 445101213886 q^{49} + 159045713302 q^{50} - 752541530718 q^{51} - 1258646652384 q^{52} + 163491194450 q^{53} + 280492434036 q^{54} + 2316003716734 q^{55} + 1401137247720 q^{56} - 3512103111582 q^{57} - 2043563861164 q^{58} + 1390928871798 q^{59} + 2538865068838 q^{60} + 1206712743316 q^{61} - 797102503680 q^{62} + 1592924350020 q^{63} - 4349266259082 q^{64} - 6887523079836 q^{65} - 6066573198828 q^{66} + 4897880955846 q^{67} + 9263697501104 q^{68} + 5591463008389 q^{69} + 122583681980 q^{70} - 11807369705652 q^{71} - 14860679670686 q^{72} + 11370214585220 q^{73} + 4697559217974 q^{74} - 1153651030698 q^{75} - 3439851431952 q^{76} + 2354023454730 q^{77} + 13113195774364 q^{78} + 25788000795960 q^{79} - 1478065433778 q^{80} - 2677157227201 q^{81} - 39249706826630 q^{82} - 21176863066294 q^{83} - 9066795239964 q^{84} + 23954611176336 q^{85} + 58980508269280 q^{86} + 31085689530096 q^{87} + 14220375308982 q^{88} - 17651403495548 q^{89} - 26661428655188 q^{90} - 65390356485788 q^{91} - 25437778383110 q^{92} + 47451217324395 q^{93} - 6584235596320 q^{94} + 10342203568182 q^{95} - 34412893203212 q^{96} + 59528636795546 q^{97} + 51939574101896 q^{98} + 9186161081045 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(33))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
33.14.a \(\chi_{33}(1, \cdot)\) 33.14.a.a 1 1
33.14.a.b 4
33.14.a.c 4
33.14.a.d 5
33.14.a.e 6
33.14.d \(\chi_{33}(32, \cdot)\) 33.14.d.a 2 1
33.14.d.b 48
33.14.e \(\chi_{33}(4, \cdot)\) n/a 104 4
33.14.f \(\chi_{33}(2, \cdot)\) n/a 200 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)