# Properties

 Label 2475.2.c Level $2475$ Weight $2$ Character orbit 2475.c Rep. character $\chi_{2475}(199,\cdot)$ Character field $\Q$ Dimension $76$ Newform subspaces $20$ Sturm bound $720$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2475 = 3^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2475.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$20$$ Sturm bound: $$720$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2475, [\chi])$$.

Total New Old
Modular forms 384 76 308
Cusp forms 336 76 260
Eisenstein series 48 0 48

## Trace form

 $$76 q - 86 q^{4} + O(q^{10})$$ $$76 q - 86 q^{4} - 4 q^{11} - 4 q^{14} + 98 q^{16} - 12 q^{19} - 8 q^{26} - 40 q^{29} + 22 q^{31} + 28 q^{34} + 40 q^{41} + 18 q^{44} - 72 q^{46} - 48 q^{49} + 36 q^{56} + 26 q^{59} + 12 q^{61} - 94 q^{64} - 98 q^{71} + 48 q^{74} - 12 q^{76} + 32 q^{79} - 16 q^{86} - 50 q^{89} - 76 q^{91} + 112 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2475, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2475.2.c.a $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}-2iq^{7}-q^{11}-4iq^{13}+\cdots$$
2475.2.c.b $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}-q^{11}+\cdots$$
2475.2.c.c $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}-3iq^{7}+3iq^{8}-q^{11}+\cdots$$
2475.2.c.d $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}-q^{11}+\cdots$$
2475.2.c.e $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{7}+3iq^{8}+q^{11}+\cdots$$
2475.2.c.f $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+3iq^{8}+q^{11}+2iq^{13}+\cdots$$
2475.2.c.g $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}-2iq^{7}+3iq^{8}+q^{11}+\cdots$$
2475.2.c.h $2$ $19.763$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+iq^{7}+q^{11}-iq^{13}+4q^{16}+\cdots$$
2475.2.c.i $4$ $19.763$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$$
2475.2.c.j $4$ $19.763$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$$
2475.2.c.k $4$ $19.763$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$$
2475.2.c.l $4$ $19.763$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
2475.2.c.m $4$ $19.763$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}-2\zeta_{8}^{2}q^{7}+\cdots$$
2475.2.c.n $4$ $19.763$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}-q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots$$
2475.2.c.o $4$ $19.763$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
2475.2.c.p $4$ $19.763$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots$$
2475.2.c.q $6$ $19.763$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{4})q^{2}+(-3-\beta _{1})q^{4}+(\beta _{3}+\cdots)q^{7}+\cdots$$
2475.2.c.r $6$ $19.763$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$$
2475.2.c.s $8$ $19.763$ 8.0.9488318464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$$
2475.2.c.t $8$ $19.763$ 8.0.9488318464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2475, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2475, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(495, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(825, [\chi])$$$$^{\oplus 2}$$