Properties

 Label 1638.2.c Level $1638$ Weight $2$ Character orbit 1638.c Rep. character $\chi_{1638}(883,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $11$ Sturm bound $672$ Trace bound $14$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1638.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$11$$ Sturm bound: $$672$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$17$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1638, [\chi])$$.

Total New Old
Modular forms 352 36 316
Cusp forms 320 36 284
Eisenstein series 32 0 32

Trace form

 $$36 q - 36 q^{4} + O(q^{10})$$ $$36 q - 36 q^{4} + 4 q^{13} - 4 q^{14} + 36 q^{16} - 8 q^{17} + 4 q^{22} - 4 q^{23} - 20 q^{25} - 40 q^{29} - 8 q^{35} + 32 q^{38} - 24 q^{43} - 36 q^{49} - 4 q^{52} - 32 q^{53} + 8 q^{55} + 4 q^{56} - 8 q^{61} - 24 q^{62} - 36 q^{64} + 36 q^{65} + 8 q^{68} + 4 q^{74} - 8 q^{77} + 4 q^{79} + 16 q^{82} - 4 q^{88} + 16 q^{91} + 4 q^{92} - 8 q^{94} - 24 q^{95} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1638, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1638.2.c.a $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots$$
1638.2.c.b $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots$$
1638.2.c.c $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+2iq^{5}+iq^{7}-iq^{8}+\cdots$$
1638.2.c.d $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots$$
1638.2.c.e $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots$$
1638.2.c.f $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{5}+iq^{7}+iq^{8}+\cdots$$
1638.2.c.g $2$ $13.079$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+3iq^{5}+iq^{7}+iq^{8}+\cdots$$
1638.2.c.h $4$ $13.079$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$$
1638.2.c.i $6$ $13.079$ 6.0.30647296.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots$$
1638.2.c.j $6$ $13.079$ 6.0.3356224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\beta _{1}q^{7}+\cdots$$
1638.2.c.k $6$ $13.079$ 6.0.3356224.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}-\beta _{1}q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1638, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1638, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(234, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(546, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(819, [\chi])$$$$^{\oplus 2}$$