# Properties

 Label 2352.3.f Level $2352$ Weight $3$ Character orbit 2352.f Rep. character $\chi_{2352}(97,\cdot)$ Character field $\Q$ Dimension $80$ Newform subspaces $13$ Sturm bound $1344$ Trace bound $23$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2352.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$1344$$ Trace bound: $$23$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(2352, [\chi])$$.

Total New Old
Modular forms 944 80 864
Cusp forms 848 80 768
Eisenstein series 96 0 96

## Trace form

 $$80 q - 240 q^{9} + O(q^{10})$$ $$80 q - 240 q^{9} + 32 q^{11} + 160 q^{23} - 416 q^{25} - 32 q^{29} + 96 q^{37} - 48 q^{39} - 64 q^{43} + 128 q^{53} - 48 q^{57} + 160 q^{65} + 384 q^{67} - 128 q^{71} + 176 q^{79} + 720 q^{81} + 32 q^{85} - 96 q^{93} - 576 q^{95} - 96 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(2352, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2352.3.f.a $2$ $64.087$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3q^{9}-15q^{11}+\cdots$$
2352.3.f.b $2$ $64.087$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-3q^{9}-10q^{11}+\cdots$$
2352.3.f.c $2$ $64.087$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{3}-\zeta_{6}q^{5}-3q^{9}+3q^{11}-4\zeta_{6}q^{13}+\cdots$$
2352.3.f.d $2$ $64.087$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3q^{9}+11q^{11}+\cdots$$
2352.3.f.e $4$ $64.087$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{1}+2\beta _{2})q^{5}-3q^{9}+\cdots$$
2352.3.f.f $4$ $64.087$ $$\Q(\sqrt{-3}, \sqrt{65})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2})q^{5}-3q^{9}+(8+\cdots)q^{11}+\cdots$$
2352.3.f.g $8$ $64.087$ 8.0.$$\cdots$$.9 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{7})q^{5}-3q^{9}+(-5+\cdots)q^{11}+\cdots$$
2352.3.f.h $8$ $64.087$ 8.0.339738624.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+(2\beta _{2}-\beta _{5}-\beta _{7})q^{5}-3q^{9}+\cdots$$
2352.3.f.i $8$ $64.087$ 8.0.339738624.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(-\beta _{4}-2\beta _{5})q^{5}-3q^{9}+\cdots$$
2352.3.f.j $8$ $64.087$ 8.0.339738624.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{4}+\beta _{5})q^{5}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
2352.3.f.k $8$ $64.087$ 8.0.$$\cdots$$.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}-3q^{9}+(3+\cdots)q^{11}+\cdots$$
2352.3.f.l $8$ $64.087$ 8.0.339738624.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{6}+\beta _{7})q^{5}-3q^{9}+(8+\cdots)q^{11}+\cdots$$
2352.3.f.m $16$ $64.087$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-\beta _{2}+\beta _{11})q^{5}-3q^{9}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(2352, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(2352, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 20}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(294, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(392, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(588, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(784, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1176, [\chi])$$$$^{\oplus 2}$$