# Properties

 Label 1200.2.f Level $1200$ Weight $2$ Character orbit 1200.f Rep. character $\chi_{1200}(49,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $9$ Sturm bound $480$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1200.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$480$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1200, [\chi])$$.

Total New Old
Modular forms 276 18 258
Cusp forms 204 18 186
Eisenstein series 72 0 72

## Trace form

 $$18 q - 18 q^{9} + O(q^{10})$$ $$18 q - 18 q^{9} - 20 q^{19} + 4 q^{29} - 4 q^{31} + 8 q^{39} + 20 q^{41} - 26 q^{49} + 20 q^{51} - 32 q^{59} - 20 q^{61} + 16 q^{69} + 32 q^{71} + 18 q^{81} - 36 q^{89} + 68 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1200, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1200.2.f.a $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}-6q^{11}-5iq^{13}+\cdots$$
1200.2.f.b $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}+2iq^{13}+2iq^{17}+\cdots$$
1200.2.f.c $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}-2q^{11}-3iq^{13}+\cdots$$
1200.2.f.d $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots$$
1200.2.f.e $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-2iq^{13}+6iq^{17}+\cdots$$
1200.2.f.f $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots$$
1200.2.f.g $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+4q^{11}-6iq^{13}-6iq^{17}+\cdots$$
1200.2.f.h $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+4q^{11}-2iq^{13}-2iq^{17}+\cdots$$
1200.2.f.i $2$ $9.582$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+5iq^{7}-q^{9}+6q^{11}+3iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1200, [\chi])$$ into lower level spaces

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