# Properties

 Label 3264.2.c Level $3264$ Weight $2$ Character orbit 3264.c Rep. character $\chi_{3264}(577,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $18$ Sturm bound $1152$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3264 = 2^{6} \cdot 3 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3264.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$1152$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$13$$, $$19$$, $$43$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3264, [\chi])$$.

Total New Old
Modular forms 600 72 528
Cusp forms 552 72 480
Eisenstein series 48 0 48

## Trace form

 $$72q - 72q^{9} + O(q^{10})$$ $$72q - 72q^{9} - 8q^{17} - 88q^{25} - 72q^{49} - 32q^{69} + 96q^{77} + 72q^{81} - 32q^{85} - 16q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3264, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3264.2.c.a $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{5}-2iq^{7}-q^{9}+3iq^{11}+\cdots$$
3264.2.c.b $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{5}+2iq^{7}-q^{9}-3iq^{11}+\cdots$$
3264.2.c.c $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{5}-2iq^{7}-q^{9}-2q^{13}+\cdots$$
3264.2.c.d $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-4iq^{7}-q^{9}-4iq^{11}-2q^{13}+\cdots$$
3264.2.c.e $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-4iq^{7}-q^{9}-4iq^{11}-2q^{13}+\cdots$$
3264.2.c.f $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2iq^{5}+2iq^{7}-q^{9}-2q^{13}+\cdots$$
3264.2.c.g $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{5}-2iq^{7}-q^{9}-5iq^{11}+\cdots$$
3264.2.c.h $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{5}+2iq^{7}-q^{9}+5iq^{11}+\cdots$$
3264.2.c.i $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2iq^{5}-2iq^{7}-q^{9}+6q^{13}+\cdots$$
3264.2.c.j $$2$$ $$26.063$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2iq^{5}+2iq^{7}-q^{9}+6q^{13}+\cdots$$
3264.2.c.k $$4$$ $$26.063$$ $$\Q(i, \sqrt{33})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots$$
3264.2.c.l $$4$$ $$26.063$$ $$\Q(i, \sqrt{33})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+2\beta _{2}q^{7}-q^{9}+\cdots$$
3264.2.c.m $$4$$ $$26.063$$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}-4\beta _{1}q^{7}-q^{9}+3\beta _{1}q^{11}+\cdots$$
3264.2.c.n $$6$$ $$26.063$$ 6.0.399424.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
3264.2.c.o $$6$$ $$26.063$$ 6.0.399424.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$$
3264.2.c.p $$8$$ $$26.063$$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{3}q^{5}-q^{9}+(3\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots$$
3264.2.c.q $$10$$ $$26.063$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}+\beta _{9}q^{5}+\beta _{3}q^{7}-q^{9}+(\beta _{6}+\cdots)q^{11}+\cdots$$
3264.2.c.r $$10$$ $$26.063$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{9}q^{5}-\beta _{3}q^{7}-q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3264, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3264, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(51, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(68, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(102, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(136, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(204, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(272, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(408, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(544, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(816, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1088, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1632, [\chi])$$$$^{\oplus 2}$$