# Properties

 Label 1100.6.b Level $1100$ Weight $6$ Character orbit 1100.b Rep. character $\chi_{1100}(749,\cdot)$ Character field $\Q$ Dimension $74$ Newform subspaces $9$ Sturm bound $1080$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1100 = 2^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 1100.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$1080$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(1100, [\chi])$$.

Total New Old
Modular forms 918 74 844
Cusp forms 882 74 808
Eisenstein series 36 0 36

## Trace form

 $$74 q - 4972 q^{9} + O(q^{10})$$ $$74 q - 4972 q^{9} - 242 q^{11} - 1220 q^{19} - 608 q^{21} + 21004 q^{29} - 10854 q^{31} + 25196 q^{39} + 64908 q^{41} - 186366 q^{49} + 92716 q^{51} - 122934 q^{59} - 40560 q^{61} - 248638 q^{69} + 235342 q^{71} - 56984 q^{79} + 445258 q^{81} + 320274 q^{89} + 125900 q^{91} + 173756 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(1100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1100.6.b.a $2$ $176.422$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+7iq^{3}+50iq^{7}+194q^{9}+11^{2}q^{11}+\cdots$$
1100.6.b.b $4$ $176.422$ $$\Q(i, \sqrt{1761})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}-5\beta _{2})q^{3}+(5\beta _{1}+34\beta _{2})q^{7}+\cdots$$
1100.6.b.c $4$ $176.422$ $$\Q(i, \sqrt{31})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-3\beta _{1}+\beta _{3})q^{3}+(-134\beta _{1}+3\beta _{3})q^{7}+\cdots$$
1100.6.b.d $6$ $176.422$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+(-24\beta _{3}+7\beta _{4}+2\beta _{5})q^{7}+\cdots$$
1100.6.b.e $8$ $176.422$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+(-6\beta _{2}+\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots$$
1100.6.b.f $8$ $176.422$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(3\beta _{1}-\beta _{2}-\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots$$
1100.6.b.g $10$ $176.422$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}+(-\beta _{5}+2\beta _{6}+\beta _{8})q^{7}+(-94+\cdots)q^{9}+\cdots$$
1100.6.b.h $16$ $176.422$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{3}+(-2\beta _{8}+4\beta _{9}-\beta _{10})q^{7}+\cdots$$
1100.6.b.i $16$ $176.422$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{8}+\beta _{9})q^{3}+(-2\beta _{9}+\beta _{10})q^{7}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(1100, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(1100, [\chi]) \simeq$$ $$S_{6}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(220, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(550, [\chi])$$$$^{\oplus 2}$$