# Properties

 Label 24.19.e Level $24$ Weight $19$ Character orbit 24.e Rep. character $\chi_{24}(17,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $1$ Sturm bound $76$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ $$=$$ $$19$$ Character orbit: $$[\chi]$$ $$=$$ 24.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$76$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{19}(24, [\chi])$$.

Total New Old
Modular forms 76 18 58
Cusp forms 68 18 50
Eisenstein series 8 0 8

## Trace form

 $$18 q - 13870 q^{3} - 33970284 q^{7} - 118672382 q^{9} + O(q^{10})$$ $$18 q - 13870 q^{3} - 33970284 q^{7} - 118672382 q^{9} - 18718026444 q^{13} - 64466484448 q^{15} + 717309742500 q^{19} + 211690660116 q^{21} - 8665511326974 q^{25} + 3650541535394 q^{27} - 700541980812 q^{31} + 45242709621536 q^{33} + 56821562236692 q^{37} + 66941158917812 q^{39} - 976753869605820 q^{43} + 211880296865344 q^{45} + 1057370959348758 q^{49} + 2443235643908992 q^{51} + 5012796209236416 q^{55} - 8853486423554780 q^{57} + 6658107062441076 q^{61} - 10444823492751372 q^{63} + 12267592236710820 q^{67} + 41175698395034048 q^{69} - 4774971621100860 q^{73} + 39251780686403266 q^{75} - 62992818987441228 q^{79} - 156484925985567182 q^{81} - 130908551190660864 q^{85} + 219496030991618400 q^{87} + 531416138686075080 q^{91} + 698957907570060532 q^{93} - 1034392673337699996 q^{97} - 1550110114668532160 q^{99} + O(q^{100})$$

## Decomposition of $$S_{19}^{\mathrm{new}}(24, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.19.e.a $18$ $49.293$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$-13870$$ $$0$$ $$-33970284$$ $$q+(-771+\beta _{1})q^{3}+(-4+9\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{19}^{\mathrm{old}}(24, [\chi])$$ into lower level spaces

$$S_{19}^{\mathrm{old}}(24, [\chi]) \simeq$$ $$S_{19}^{\mathrm{new}}(3, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{19}^{\mathrm{new}}(6, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{19}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 2}$$