Properties

 Label 1152.2.c Level $1152$ Weight $2$ Character orbit 1152.c Rep. character $\chi_{1152}(1151,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $384$ Trace bound $35$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$384$$ Trace bound: $$35$$ Distinguishing $$T_p$$: $$23$$, $$37$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1152, [\chi])$$.

Total New Old
Modular forms 224 16 208
Cusp forms 160 16 144
Eisenstein series 64 0 64

Trace form

 $$16 q + O(q^{10})$$ $$16 q - 16 q^{25} - 80 q^{49} + 64 q^{73} + 128 q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1152, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.2.c.a $4$ $9.199$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$$
1152.2.c.b $4$ $9.199$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots$$
1152.2.c.c $4$ $9.199$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$$
1152.2.c.d $4$ $9.199$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1152, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1152, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$