Properties

 Label 450.4.c Level $450$ Weight $4$ Character orbit 450.c Rep. character $\chi_{450}(199,\cdot)$ Character field $\Q$ Dimension $22$ Newform subspaces $11$ Sturm bound $360$ Trace bound $14$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$450 = 2 \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 450.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$11$$ Sturm bound: $$360$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$7$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(450, [\chi])$$.

Total New Old
Modular forms 294 22 272
Cusp forms 246 22 224
Eisenstein series 48 0 48

Trace form

 $$22 q - 88 q^{4} + O(q^{10})$$ $$22 q - 88 q^{4} + 90 q^{11} - 136 q^{14} + 352 q^{16} + 82 q^{19} - 32 q^{26} - 816 q^{29} - 460 q^{31} + 204 q^{34} + 294 q^{41} - 360 q^{44} - 360 q^{46} + 282 q^{49} + 544 q^{56} + 480 q^{59} + 1076 q^{61} - 1408 q^{64} - 600 q^{71} - 712 q^{74} - 328 q^{76} - 6260 q^{79} + 2464 q^{86} + 318 q^{89} + 4984 q^{91} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(450, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
450.4.c.a $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}-4q^{4}+iq^{7}+8iq^{8}-42q^{11}+\cdots$$
450.4.c.b $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}-4q^{4}+11iq^{7}+8iq^{8}+\cdots$$
450.4.c.c $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-4q^{4}+34iq^{7}-8iq^{8}+\cdots$$
450.4.c.d $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-4q^{4}+2iq^{7}-4iq^{8}-12q^{11}+\cdots$$
450.4.c.e $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-4q^{4}+8iq^{7}+4iq^{8}-12q^{11}+\cdots$$
450.4.c.f $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-4q^{4}+7iq^{7}-4iq^{8}-6q^{11}+\cdots$$
450.4.c.g $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-4q^{4}+7iq^{7}+4iq^{8}+6q^{11}+\cdots$$
450.4.c.h $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}-4q^{4}+23iq^{7}+8iq^{8}+\cdots$$
450.4.c.i $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-4q^{4}+11iq^{7}-8iq^{8}+\cdots$$
450.4.c.j $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-4q^{4}+2iq^{7}-4iq^{8}+48q^{11}+\cdots$$
450.4.c.k $2$ $26.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-4q^{4}+2^{4}iq^{7}-4iq^{8}+60q^{11}+\cdots$$

Decomposition of $$S_{4}^{\mathrm{old}}(450, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(450, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$