Properties

 Label 225.4.k Level $225$ Weight $4$ Character orbit 225.k Rep. character $\chi_{225}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $104$ Newform subspaces $5$ Sturm bound $120$ Trace bound $4$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$45$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$120$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(225, [\chi])$$.

Total New Old
Modular forms 192 112 80
Cusp forms 168 104 64
Eisenstein series 24 8 16

Trace form

 $$104 q + 202 q^{4} - 4 q^{6} + 64 q^{9} + O(q^{10})$$ $$104 q + 202 q^{4} - 4 q^{6} + 64 q^{9} - 98 q^{11} - 6 q^{14} - 754 q^{16} + 8 q^{19} - 78 q^{21} - 510 q^{24} + 1192 q^{26} + 682 q^{29} + 34 q^{31} - 378 q^{34} - 128 q^{36} - 58 q^{39} - 502 q^{41} - 4664 q^{44} + 1104 q^{46} + 2358 q^{49} + 68 q^{51} + 6682 q^{54} - 2052 q^{56} + 1964 q^{59} + 34 q^{61} - 6512 q^{64} + 8254 q^{66} - 1026 q^{69} + 2240 q^{71} + 4612 q^{74} - 1214 q^{76} + 686 q^{79} + 440 q^{81} - 5682 q^{84} - 9494 q^{86} - 10272 q^{89} + 2372 q^{91} + 402 q^{94} - 17516 q^{96} - 136 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(225, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.4.k.a $8$ $13.275$ 8.0.303595776.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+(3\beta _{1}+\beta _{4}+2\beta _{5}+2\beta _{7})q^{3}+\cdots$$
225.4.k.b $8$ $13.275$ 8.0.303595776.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{7})q^{2}+(\beta _{4}-\beta _{5}-\beta _{7})q^{3}+\cdots$$
225.4.k.c $12$ $13.275$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{7}+\beta _{11})q^{2}+(\beta _{5}+\beta _{8}+\beta _{11})q^{3}+\cdots$$
225.4.k.d $28$ $13.275$ None $$0$$ $$0$$ $$0$$ $$0$$
225.4.k.e $48$ $13.275$ None $$0$$ $$0$$ $$0$$ $$0$$

Decomposition of $$S_{4}^{\mathrm{old}}(225, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(225, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$