# Properties

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

# Related objects

## 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: $$\Q$$ Newform subspaces: $$1$$ 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

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

## Decomposition of $$S_{19}^{\mathrm{new}}(6, [\chi])$$ into newform subspaces

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

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