Properties

Label 3.23.b
Level 3
Weight 23
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 7
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 23 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(3, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

Trace form

\(6q \) \(\mathstrut +\mathstrut 86670q^{3} \) \(\mathstrut -\mathstrut 11258688q^{4} \) \(\mathstrut +\mathstrut 293575104q^{6} \) \(\mathstrut -\mathstrut 3447063060q^{7} \) \(\mathstrut +\mathstrut 57339715158q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 86670q^{3} \) \(\mathstrut -\mathstrut 11258688q^{4} \) \(\mathstrut +\mathstrut 293575104q^{6} \) \(\mathstrut -\mathstrut 3447063060q^{7} \) \(\mathstrut +\mathstrut 57339715158q^{9} \) \(\mathstrut -\mathstrut 186869600640q^{10} \) \(\mathstrut -\mathstrut 1325972980800q^{12} \) \(\mathstrut +\mathstrut 2025132496860q^{13} \) \(\mathstrut +\mathstrut 2628031314240q^{15} \) \(\mathstrut -\mathstrut 9703467227136q^{16} \) \(\mathstrut +\mathstrut 42127150135680q^{18} \) \(\mathstrut +\mathstrut 100485688668636q^{19} \) \(\mathstrut -\mathstrut 789079193287812q^{21} \) \(\mathstrut +\mathstrut 1045890315676800q^{22} \) \(\mathstrut -\mathstrut 2472467233277952q^{24} \) \(\mathstrut +\mathstrut 1396569263732790q^{25} \) \(\mathstrut -\mathstrut 10731657558901410q^{27} \) \(\mathstrut +\mathstrut 44570708098492800q^{28} \) \(\mathstrut -\mathstrut 116169123436801920q^{30} \) \(\mathstrut +\mathstrut 114109662401153292q^{31} \) \(\mathstrut -\mathstrut 174850022773609920q^{33} \) \(\mathstrut +\mathstrut 319017868488396288q^{34} \) \(\mathstrut -\mathstrut 707589966262651200q^{36} \) \(\mathstrut +\mathstrut 683782874080661820q^{37} \) \(\mathstrut -\mathstrut 1038045209126993748q^{39} \) \(\mathstrut +\mathstrut 1781949720499015680q^{40} \) \(\mathstrut -\mathstrut 1108714403505421440q^{42} \) \(\mathstrut +\mathstrut 273273330169769340q^{43} \) \(\mathstrut +\mathstrut 3228622736179443840q^{45} \) \(\mathstrut -\mathstrut 8349686917048426752q^{46} \) \(\mathstrut +\mathstrut 10392767955626526720q^{48} \) \(\mathstrut -\mathstrut 8294807529216677070q^{49} \) \(\mathstrut +\mathstrut 14237699192275302144q^{51} \) \(\mathstrut -\mathstrut 22636595958302682240q^{52} \) \(\mathstrut +\mathstrut 48383805955937626944q^{54} \) \(\mathstrut -\mathstrut 40874587160137441920q^{55} \) \(\mathstrut +\mathstrut 43721391850797114540q^{57} \) \(\mathstrut -\mathstrut 67285958146132360320q^{58} \) \(\mathstrut -\mathstrut 44311576503733309440q^{60} \) \(\mathstrut +\mathstrut 121649250388145492892q^{61} \) \(\mathstrut -\mathstrut 184494903535705683060q^{63} \) \(\mathstrut +\mathstrut 285203601894474055680q^{64} \) \(\mathstrut -\mathstrut 374640791614422030720q^{66} \) \(\mathstrut +\mathstrut 75701571086175260700q^{67} \) \(\mathstrut -\mathstrut 233446021721582921856q^{69} \) \(\mathstrut +\mathstrut 1113607014897000234240q^{70} \) \(\mathstrut -\mathstrut 639860863731149721600q^{72} \) \(\mathstrut -\mathstrut 57178481309533986900q^{73} \) \(\mathstrut -\mathstrut 333973626119358339330q^{75} \) \(\mathstrut -\mathstrut 731229802672243966080q^{76} \) \(\mathstrut +\mathstrut 735750453969076417920q^{78} \) \(\mathstrut +\mathstrut 384537395891327736396q^{79} \) \(\mathstrut +\mathstrut 3109769787236091157926q^{81} \) \(\mathstrut -\mathstrut 5166859472437001068800q^{82} \) \(\mathstrut +\mathstrut 6698665889827068753792q^{84} \) \(\mathstrut -\mathstrut 6772579853411844011520q^{85} \) \(\mathstrut +\mathstrut 4995406256507248236480q^{87} \) \(\mathstrut -\mathstrut 404168025320661381120q^{88} \) \(\mathstrut -\mathstrut 3858783621100493362560q^{90} \) \(\mathstrut -\mathstrut 2806742501496183911304q^{91} \) \(\mathstrut +\mathstrut 2087220280517252053020q^{93} \) \(\mathstrut +\mathstrut 8135725180445469439488q^{94} \) \(\mathstrut -\mathstrut 15069021592890694238208q^{96} \) \(\mathstrut +\mathstrut 1565231688506989945740q^{97} \) \(\mathstrut -\mathstrut 6095367699696122981760q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{23}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.23.b.a \(6\) \(9.201\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(86670\) \(0\) \(-3447063060\) \(q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots\)