# Properties

 Label 2200.2.b Level $2200$ Weight $2$ Character orbit 2200.b Rep. character $\chi_{2200}(1849,\cdot)$ Character field $\Q$ Dimension $46$ Newform subspaces $13$ Sturm bound $720$ Trace bound $19$

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## Defining parameters

 Level: $$N$$ $$=$$ $$2200 = 2^{3} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2200.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$720$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2200, [\chi])$$.

Total New Old
Modular forms 384 46 338
Cusp forms 336 46 290
Eisenstein series 48 0 48

## Trace form

 $$46 q - 42 q^{9} + O(q^{10})$$ $$46 q - 42 q^{9} - 6 q^{11} + 16 q^{21} - 28 q^{29} - 16 q^{39} - 4 q^{41} - 30 q^{49} + 24 q^{51} + 20 q^{59} - 44 q^{61} - 20 q^{69} - 16 q^{71} + 40 q^{79} + 14 q^{81} - 52 q^{89} - 32 q^{91} + 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2200, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2200.2.b.a $2$ $17.567$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-6iq^{17}+\cdots$$
2200.2.b.b $2$ $17.567$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}-iq^{7}-6q^{9}-q^{11}-6iq^{13}+\cdots$$
2200.2.b.c $2$ $17.567$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+3q^{9}-q^{11}-3iq^{13}-3iq^{17}+\cdots$$
2200.2.b.d $2$ $17.567$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{9}-q^{11}+8q^{19}-4iq^{23}+\cdots$$
2200.2.b.e $2$ $17.567$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+3q^{9}+q^{11}+2iq^{13}-2iq^{17}+\cdots$$
2200.2.b.f $4$ $17.567$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots$$
2200.2.b.g $4$ $17.567$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots$$
2200.2.b.h $4$ $17.567$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots$$
2200.2.b.i $4$ $17.567$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+q^{11}+\cdots$$
2200.2.b.j $4$ $17.567$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$$
2200.2.b.k $4$ $17.567$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$$
2200.2.b.l $6$ $17.567$ 6.0.44836416.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots$$
2200.2.b.m $6$ $17.567$ 6.0.96668224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2200, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2200, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(220, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(440, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(550, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1100, [\chi])$$$$^{\oplus 2}$$