Properties

Label 6.19
Level 6
Weight 19
Dimension 6
Nonzero newspaces 1
Newforms 1
Sturm bound 38
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(38\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(6))\).

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

Trace form

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

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.19.b \(\chi_{6}(5, \cdot)\) 6.19.b.a 6 1

Decomposition of \(S_{19}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{19}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{19}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)