# Properties

 Label 12.4.b Level $12$ Weight $4$ Character orbit 12.b Rep. character $\chi_{12}(11,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 12.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(12, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

## Trace form

 $$4 q - 8 q^{4} - 24 q^{6} - 12 q^{9} + O(q^{10})$$ $$4 q - 8 q^{4} - 24 q^{6} - 12 q^{9} + 80 q^{10} + 120 q^{12} - 40 q^{13} - 224 q^{16} - 240 q^{18} + 120 q^{21} + 240 q^{22} + 288 q^{24} + 180 q^{25} - 240 q^{28} - 240 q^{30} - 480 q^{33} + 320 q^{34} + 24 q^{36} - 520 q^{37} + 320 q^{40} + 240 q^{42} + 960 q^{45} - 672 q^{46} - 480 q^{48} + 1132 q^{49} + 80 q^{52} + 792 q^{54} - 1080 q^{57} - 1360 q^{58} - 960 q^{60} - 1768 q^{61} + 1408 q^{64} + 1200 q^{66} + 1344 q^{69} + 480 q^{70} - 960 q^{72} + 1640 q^{73} + 2160 q^{76} + 240 q^{78} - 2844 q^{81} - 1120 q^{82} - 240 q^{84} - 1280 q^{85} - 2880 q^{88} - 240 q^{90} + 3480 q^{93} - 1344 q^{94} + 384 q^{96} + 3080 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(12, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.4.b.a $4$ $0.708$ $$\Q(\sqrt{3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$$