# Properties

 Label 2400.2.f Level $2400$ Weight $2$ Character orbit 2400.f Rep. character $\chi_{2400}(1249,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $18$ Sturm bound $960$ Trace bound $31$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2400 = 2^{5} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2400.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$960$$ Trace bound: $$31$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$, $$19$$, $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2400, [\chi])$$.

Total New Old
Modular forms 528 36 492
Cusp forms 432 36 396
Eisenstein series 96 0 96

## Trace form

 $$36q - 36q^{9} + O(q^{10})$$ $$36q - 36q^{9} - 8q^{29} - 56q^{41} - 20q^{49} + 8q^{61} + 36q^{81} + 56q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2400, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2400.2.f.a $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-4q^{11}+2iq^{13}+\cdots$$
2400.2.f.b $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}-4q^{11}+7iq^{13}+\cdots$$
2400.2.f.c $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots$$
2400.2.f.d $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-4q^{11}-6iq^{13}+\cdots$$
2400.2.f.e $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}+2iq^{13}+2iq^{17}+\cdots$$
2400.2.f.f $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}-5iq^{13}-5q^{19}+\cdots$$
2400.2.f.g $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+2iq^{13}-6iq^{17}-4q^{19}+\cdots$$
2400.2.f.h $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}-iq^{13}-3q^{19}+\cdots$$
2400.2.f.i $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-2iq^{13}+6iq^{17}+\cdots$$
2400.2.f.j $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}+2iq^{13}-6iq^{17}+\cdots$$
2400.2.f.k $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}+iq^{13}+3q^{19}+\cdots$$
2400.2.f.l $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}-2iq^{13}+6iq^{17}+4q^{19}+\cdots$$
2400.2.f.m $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}+5iq^{13}+5q^{19}+\cdots$$
2400.2.f.n $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots$$
2400.2.f.o $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}+4q^{11}+6iq^{13}+\cdots$$
2400.2.f.p $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots$$
2400.2.f.q $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}+4q^{11}-7iq^{13}+\cdots$$
2400.2.f.r $$2$$ $$19.164$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+4q^{11}-2iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2400, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2400, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(600, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(800, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1200, [\chi])$$$$^{\oplus 2}$$