Properties

Label 3.33.b
Level 3
Weight 33
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 33 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(3, [\chi])\).

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

Trace form

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

Decomposition of \(S_{33}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.33.b.a \(10\) \(19.460\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-21387150\) \(0\) \(-5\!\cdots\!40\) \(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)