# Properties

 Label 1100.4.b Level $1100$ Weight $4$ Character orbit 1100.b Rep. character $\chi_{1100}(749,\cdot)$ Character field $\Q$ Dimension $46$ Newform subspaces $10$ Sturm bound $720$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1100 = 2^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1100.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$720$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1100, [\chi])$$.

Total New Old
Modular forms 558 46 512
Cusp forms 522 46 476
Eisenstein series 36 0 36

## Trace form

 $$46 q - 538 q^{9} + O(q^{10})$$ $$46 q - 538 q^{9} + 22 q^{11} + 72 q^{19} + 208 q^{21} - 236 q^{29} + 212 q^{31} + 200 q^{39} + 924 q^{41} - 1886 q^{49} - 1664 q^{51} - 300 q^{61} - 748 q^{69} - 452 q^{71} - 104 q^{79} + 4750 q^{81} - 324 q^{89} + 1320 q^{91} - 814 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1100.4.b.a $2$ $64.902$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{3}-12iq^{7}-37q^{9}-11q^{11}+\cdots$$
1100.4.b.b $2$ $64.902$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+5iq^{3}+11iq^{7}+2q^{9}-11q^{11}+\cdots$$
1100.4.b.c $2$ $64.902$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+5iq^{3}-26iq^{7}+2q^{9}-11q^{11}+\cdots$$
1100.4.b.d $2$ $64.902$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+5iq^{3}+19iq^{7}+2q^{9}-11q^{11}+\cdots$$
1100.4.b.e $4$ $64.902$ $$\Q(i, \sqrt{97})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-2\beta _{2})q^{3}+(6\beta _{1}+4\beta _{2})q^{7}+(-22+\cdots)q^{9}+\cdots$$
1100.4.b.f $4$ $64.902$ $$\Q(i, \sqrt{97})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-2\beta _{2})q^{3}+(\beta _{1}+4\beta _{2})q^{7}+(-22+\cdots)q^{9}+\cdots$$
1100.4.b.g $4$ $64.902$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{1}-\beta _{2})q^{3}+(9\beta _{1}-2\beta _{2})q^{7}+(-13+\cdots)q^{9}+\cdots$$
1100.4.b.h $6$ $64.902$ 6.0.1351885824.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$$
1100.4.b.i $10$ $64.902$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(-12-\beta _{2})q^{9}+\cdots$$
1100.4.b.j $10$ $64.902$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(\beta _{3}+2\beta _{6}-\beta _{7})q^{7}+(-12+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(1100, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1100, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(220, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(550, [\chi])$$$$^{\oplus 2}$$