Properties

Label 6.19.b
Level 6
Weight 19
Character orbit b
Rep. character \(\chi_{6}(5,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 19
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 19 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(19\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(6, [\chi])\).

Total New Old
Modular forms 20 6 14
Cusp forms 16 6 10
Eisenstein series 4 0 4

Trace form

\(6q \) \(\mathstrut -\mathstrut 6258q^{3} \) \(\mathstrut -\mathstrut 786432q^{4} \) \(\mathstrut -\mathstrut 15753216q^{6} \) \(\mathstrut +\mathstrut 28233804q^{7} \) \(\mathstrut +\mathstrut 695971638q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 6258q^{3} \) \(\mathstrut -\mathstrut 786432q^{4} \) \(\mathstrut -\mathstrut 15753216q^{6} \) \(\mathstrut +\mathstrut 28233804q^{7} \) \(\mathstrut +\mathstrut 695971638q^{9} \) \(\mathstrut -\mathstrut 434257920q^{10} \) \(\mathstrut +\mathstrut 820248576q^{12} \) \(\mathstrut +\mathstrut 29566196220q^{13} \) \(\mathstrut +\mathstrut 119627095680q^{15} \) \(\mathstrut +\mathstrut 103079215104q^{16} \) \(\mathstrut +\mathstrut 315939373056q^{18} \) \(\mathstrut -\mathstrut 438814047012q^{19} \) \(\mathstrut +\mathstrut 2876527406172q^{21} \) \(\mathstrut -\mathstrut 2844452929536q^{22} \) \(\mathstrut +\mathstrut 2064805527552q^{24} \) \(\mathstrut -\mathstrut 25696048717290q^{25} \) \(\mathstrut +\mathstrut 11197265522814q^{27} \) \(\mathstrut -\mathstrut 3700661157888q^{28} \) \(\mathstrut +\mathstrut 13072787619840q^{30} \) \(\mathstrut +\mathstrut 21775814927148q^{31} \) \(\mathstrut -\mathstrut 962560003968q^{33} \) \(\mathstrut +\mathstrut 99067611119616q^{34} \) \(\mathstrut -\mathstrut 91222394535936q^{36} \) \(\mathstrut +\mathstrut 638446564817436q^{37} \) \(\mathstrut -\mathstrut 736541155104180q^{39} \) \(\mathstrut +\mathstrut 56919054090240q^{40} \) \(\mathstrut -\mathstrut 203954622480384q^{42} \) \(\mathstrut -\mathstrut 1688313718883652q^{43} \) \(\mathstrut +\mathstrut 390590504075520q^{45} \) \(\mathstrut +\mathstrut 1979247919104q^{46} \) \(\mathstrut -\mathstrut 107511621353472q^{48} \) \(\mathstrut -\mathstrut 895767896448270q^{49} \) \(\mathstrut +\mathstrut 9636273526722048q^{51} \) \(\mathstrut -\mathstrut 3875300470947840q^{52} \) \(\mathstrut +\mathstrut 2993011804200960q^{54} \) \(\mathstrut -\mathstrut 1259959207783680q^{55} \) \(\mathstrut +\mathstrut 4023767318253996q^{57} \) \(\mathstrut +\mathstrut 21251172660756480q^{58} \) \(\mathstrut -\mathstrut 15679762684968960q^{60} \) \(\mathstrut -\mathstrut 16279597277700036q^{61} \) \(\mathstrut -\mathstrut 32525159214131028q^{63} \) \(\mathstrut -\mathstrut 13510798882111488q^{64} \) \(\mathstrut -\mathstrut 60047751762690048q^{66} \) \(\mathstrut +\mathstrut 11153724314613276q^{67} \) \(\mathstrut +\mathstrut 3612037794746112q^{69} \) \(\mathstrut +\mathstrut 161904998736691200q^{70} \) \(\mathstrut -\mathstrut 41410805505196032q^{72} \) \(\mathstrut -\mathstrut 78910243347781140q^{73} \) \(\mathstrut +\mathstrut 348225828845090910q^{75} \) \(\mathstrut +\mathstrut 57516234769956864q^{76} \) \(\mathstrut -\mathstrut 168903906208235520q^{78} \) \(\mathstrut -\mathstrut 476518976428926228q^{79} \) \(\mathstrut +\mathstrut 630680446106425062q^{81} \) \(\mathstrut +\mathstrut 396536393269149696q^{82} \) \(\mathstrut -\mathstrut 377032200181776384q^{84} \) \(\mathstrut -\mathstrut 967978669078932480q^{85} \) \(\mathstrut +\mathstrut 419256510981966720q^{87} \) \(\mathstrut +\mathstrut 372828134380142592q^{88} \) \(\mathstrut -\mathstrut 2046848246643179520q^{90} \) \(\mathstrut -\mathstrut 1032060167365562760q^{91} \) \(\mathstrut +\mathstrut 764294136047005116q^{93} \) \(\mathstrut +\mathstrut 2566175766871080960q^{94} \) \(\mathstrut -\mathstrut 270638190107295744q^{96} \) \(\mathstrut +\mathstrut 834695417243310348q^{97} \) \(\mathstrut +\mathstrut 761688154713814272q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(6, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6.19.b.a \(6\) \(12.323\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-6258\) \(0\) \(28233804\) \(q+\beta _{1}q^{2}+(-1043+20\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{19}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{19}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{19}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)