# Properties

 Label 12.19.c Level $12$ Weight $19$ Character orbit 12.c Rep. character $\chi_{12}(5,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $38$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$19$$ Character orbit: $$[\chi]$$ $$=$$ 12.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$38$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{19}(12, [\chi])$$.

Total New Old
Modular forms 39 6 33
Cusp forms 33 6 27
Eisenstein series 6 0 6

## Trace form

 $$6 q + 23934 q^{3} + 11024364 q^{7} - 34078986 q^{9} + O(q^{10})$$ $$6 q + 23934 q^{3} + 11024364 q^{7} - 34078986 q^{9} + 1775593596 q^{13} - 9856918080 q^{15} - 202034532804 q^{19} - 200158320036 q^{21} - 5958025101930 q^{25} - 8167776022674 q^{27} - 56059471942836 q^{31} - 51478992417600 q^{33} - 167596105515108 q^{37} - 73688099161044 q^{39} + 448591926775836 q^{43} - 12918361749120 q^{45} + 3815313399549810 q^{49} + 579278365205760 q^{51} + 8271035021335680 q^{55} - 7540820577807636 q^{57} + 13350472196682684 q^{61} - 40748979535300404 q^{63} + 37560450307637244 q^{67} - 131632980577038720 q^{69} + 149418174175674348 q^{73} - 287990904570521010 q^{75} + 646522133618739468 q^{79} - 656120326335021594 q^{81} + 1416345514989166080 q^{85} - 1306513723216363200 q^{87} + 2966957008358949816 q^{91} - 2834708598841722564 q^{93} + 2984598304382259084 q^{97} - 4681229544239276160 q^{99} + O(q^{100})$$

## Decomposition of $$S_{19}^{\mathrm{new}}(12, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.19.c.a $6$ $24.646$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$23934$$ $$0$$ $$11024364$$ $$q+(3989-\beta _{1})q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots$$

## Decomposition of $$S_{19}^{\mathrm{old}}(12, [\chi])$$ into lower level spaces

$$S_{19}^{\mathrm{old}}(12, [\chi]) \simeq$$ $$S_{19}^{\mathrm{new}}(3, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{19}^{\mathrm{new}}(6, [\chi])$$$$^{\oplus 2}$$