# Properties

 Label 2175.2.c Level $2175$ Weight $2$ Character orbit 2175.c Rep. character $\chi_{2175}(349,\cdot)$ Character field $\Q$ Dimension $84$ Newform subspaces $16$ Sturm bound $600$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2175 = 3 \cdot 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2175.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$16$$ Sturm bound: $$600$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2175, [\chi])$$.

Total New Old
Modular forms 312 84 228
Cusp forms 288 84 204
Eisenstein series 24 0 24

## Trace form

 $$84 q - 92 q^{4} + 8 q^{6} - 84 q^{9} + O(q^{10})$$ $$84 q - 92 q^{4} + 8 q^{6} - 84 q^{9} + 8 q^{11} - 24 q^{14} + 124 q^{16} - 12 q^{19} - 12 q^{21} - 24 q^{24} + 8 q^{26} - 12 q^{31} - 48 q^{34} + 92 q^{36} + 20 q^{39} + 48 q^{41} - 48 q^{44} - 40 q^{46} - 136 q^{49} + 32 q^{51} - 8 q^{54} + 96 q^{56} - 72 q^{59} + 28 q^{61} - 148 q^{64} - 32 q^{66} - 32 q^{69} + 48 q^{71} + 40 q^{74} - 24 q^{76} - 24 q^{79} + 84 q^{81} + 40 q^{84} + 8 q^{86} - 72 q^{89} + 60 q^{91} + 24 q^{94} - 24 q^{96} - 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2175, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2175.2.c.a $2$ $17.367$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots$$
2175.2.c.b $2$ $17.367$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+q^{6}+4iq^{7}+\cdots$$
2175.2.c.c $2$ $17.367$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2q^{4}-iq^{7}-q^{9}-2q^{11}+\cdots$$
2175.2.c.d $2$ $17.367$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2q^{4}+2iq^{7}-q^{9}+q^{11}+\cdots$$
2175.2.c.e $2$ $17.367$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+2q^{4}-2iq^{7}-q^{9}+3q^{11}+\cdots$$
2175.2.c.f $4$ $17.367$ $$\Q(i, \sqrt{21})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$$
2175.2.c.g $4$ $17.367$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots$$
2175.2.c.h $4$ $17.367$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots$$
2175.2.c.i $4$ $17.367$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+\zeta_{8}q^{7}+\cdots$$
2175.2.c.j $4$ $17.367$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$$
2175.2.c.k $4$ $17.367$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$$
2175.2.c.l $6$ $17.367$ 6.0.3356224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots$$
2175.2.c.m $6$ $17.367$ 6.0.14077504.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}-\beta _{5}q^{6}+\cdots$$
2175.2.c.n $8$ $17.367$ 8.0.1267360000.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{5})q^{2}-\beta _{5}q^{3}+(-2+\beta _{4}+\cdots)q^{4}+\cdots$$
2175.2.c.o $14$ $17.367$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+\beta _{6}q^{6}+\cdots$$
2175.2.c.p $16$ $17.367$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2175, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2175, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(435, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(725, [\chi])$$$$^{\oplus 2}$$