Properties

Label 3.33
Level 3
Weight 33
Dimension 10
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 22
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 33 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(\Gamma_1(3))\).

Total New Old
Modular forms 12 12 0
Cusp forms 10 10 0
Eisenstein series 2 2 0

Trace form

\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} + O(q^{10}) \) \( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 7003812786596640 q^{10} - 279007424380502640 q^{12} + 567697557679805780 q^{13} - 20342205597863242080 q^{15} + 93452609752238437504 q^{16} - 546532439317269948000 q^{18} + 571007688520350419876 q^{19} - 202809296674597359852 q^{21} - 7726803521259943913760 q^{22} + 40966888307328818303616 q^{24} - 68909708350780834128950 q^{25} - 72967926462080465281230 q^{27} + 205937256056975756717600 q^{28} - 1107420825536697507876000 q^{30} + 2337947500037502285593540 q^{31} + 2522449071689961111334560 q^{33} - 6060358314194999366692224 q^{34} + 19880961335883894024618192 q^{36} - 35307903416851790686359340 q^{37} - 31624005377757923978634972 q^{39} + 103824872020641394026996480 q^{40} - 141365101025586253616004960 q^{42} + 20133134465218107006792740 q^{43} + 324508325822765233105320000 q^{45} - 1081312096716791246752963776 q^{46} + 3981901930430244196770990720 q^{48} - 2767041101974767237639509154 q^{49} + 1958591008210563208705802112 q^{51} - 5054272042223836449280397920 q^{52} + 8609682620485865645134310448 q^{54} - 11870374622399979665591304000 q^{55} + 40568829971233106153298510900 q^{57} - 126691224865576416891245282400 q^{58} + 279833341447916827662753642240 q^{60} - 196667345182223458343232398380 q^{61} + 349775312774222889759843110340 q^{63} - 738816306154787409411488427008 q^{64} + 939413077861687418842822458720 q^{66} - 442550741350999501345614861340 q^{67} + 1096443581430237499419700598208 q^{69} - 3084260511067452830890360584000 q^{70} + 5478956649034785201935062114560 q^{72} - 4530286149796751043896742263020 q^{73} + 5689646867484953837977805651250 q^{75} - 10804853453030293252172855440096 q^{76} + 9245617327241370897996048982560 q^{78} - 2115110787448996851533482223164 q^{79} - 454653247801524309158818752630 q^{81} + 6754240700896495824250705604160 q^{82} - 10589261014798101343390846457952 q^{84} + 8783873758902640422771709896960 q^{85} - 12893796544943502316879779198240 q^{87} + 15416255855088684041150976480000 q^{88} - 76437416541013126109366518121760 q^{90} + 59544256621898576615810233543816 q^{91} - 105131728169400940473110940107820 q^{93} + 301803894289991891760064059517056 q^{94} - 522680019947351351608967407401984 q^{96} + 390148965222370670128665882607700 q^{97} - 333895893109019690643343683610560 q^{99} + O(q^{100}) \)

Decomposition of \(S_{33}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd 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
3.33.b \(\chi_{3}(2, \cdot)\) 3.33.b.a 10 1