# Properties

 Label 105.3.h Level $105$ Weight $3$ Character orbit 105.h Rep. character $\chi_{105}(76,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $1$ Sturm bound $48$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(105, [\chi])$$.

Total New Old
Modular forms 36 12 24
Cusp forms 28 12 16
Eisenstein series 8 0 8

## Trace form

 $$12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} + O(q^{10})$$ $$12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(105, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.3.h.a $12$ $2.861$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-4$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(4-\beta _{1})q^{4}+\beta _{8}q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(105, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(105, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$