Properties

 Label 400.2.y Level $400$ Weight $2$ Character orbit 400.y Rep. character $\chi_{400}(129,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $56$ Newform subspaces $4$ Sturm bound $120$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 400.y (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$4$$ Sturm bound: $$120$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(400, [\chi])$$.

Total New Old
Modular forms 264 64 200
Cusp forms 216 56 160
Eisenstein series 48 8 40

Trace form

 $$56 q + 5 q^{3} - 3 q^{5} + 9 q^{9} + O(q^{10})$$ $$56 q + 5 q^{3} - 3 q^{5} + 9 q^{9} - 3 q^{11} - 5 q^{13} + 13 q^{15} - 5 q^{17} + 9 q^{19} + 6 q^{21} + 35 q^{23} + q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} - 5 q^{33} - 28 q^{35} - 30 q^{37} + q^{39} - 5 q^{41} - 7 q^{45} + 5 q^{47} - 48 q^{49} + 62 q^{51} - 10 q^{53} + 13 q^{55} + 21 q^{59} + 7 q^{61} - 30 q^{63} + 4 q^{65} - 25 q^{67} - 9 q^{69} + 17 q^{71} - 5 q^{73} - 11 q^{75} + 30 q^{77} - 7 q^{79} - 39 q^{81} - 25 q^{83} + 20 q^{85} - 55 q^{87} - 18 q^{89} - 30 q^{91} - 113 q^{95} - 25 q^{97} - 76 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(400, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
400.2.y.a $8$ $3.194$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$-10$$ $$0$$ $$q+(\zeta_{20}-\zeta_{20}^{2}-\zeta_{20}^{3}+\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots$$
400.2.y.b $8$ $3.194$ 8.0.58140625.2 None $$0$$ $$0$$ $$5$$ $$0$$ $$q+(\beta _{1}+\beta _{5}+\beta _{7})q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$$
400.2.y.c $8$ $3.194$ 8.0.58140625.2 None $$0$$ $$5$$ $$0$$ $$0$$ $$q+(1+\beta _{3}+\beta _{7})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$$
400.2.y.d $32$ $3.194$ None $$0$$ $$0$$ $$2$$ $$0$$

Decomposition of $$S_{2}^{\mathrm{old}}(400, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(400, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 2}$$