Properties

 Label 1050.3.f Level $1050$ Weight $3$ Character orbit 1050.f Rep. character $\chi_{1050}(601,\cdot)$ Character field $\Q$ Dimension $52$ Newform subspaces $5$ Sturm bound $720$ Trace bound $7$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$720$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$11$$, $$23$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1050, [\chi])$$.

Total New Old
Modular forms 504 52 452
Cusp forms 456 52 404
Eisenstein series 48 0 48

Trace form

 $$52 q + 104 q^{4} - 8 q^{7} - 156 q^{9} + O(q^{10})$$ $$52 q + 104 q^{4} - 8 q^{7} - 156 q^{9} + 24 q^{11} + 8 q^{14} + 208 q^{16} + 24 q^{21} - 72 q^{22} - 24 q^{23} - 16 q^{28} + 8 q^{29} - 312 q^{36} + 128 q^{37} + 168 q^{39} + 192 q^{43} + 48 q^{44} + 40 q^{46} - 32 q^{49} + 72 q^{51} + 88 q^{53} + 16 q^{56} - 120 q^{57} - 224 q^{58} + 24 q^{63} + 416 q^{64} + 16 q^{67} + 168 q^{71} - 224 q^{74} - 216 q^{77} + 144 q^{78} + 32 q^{79} + 468 q^{81} + 48 q^{84} + 368 q^{86} - 144 q^{88} - 28 q^{91} - 48 q^{92} - 192 q^{93} + 192 q^{98} - 72 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(1050, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1050.3.f.a $4$ $28.610$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{6}+(-2+\cdots)q^{7}+\cdots$$
1050.3.f.b $8$ $28.610$ 8.0.3317760000.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{5}q^{3}+2q^{4}-\beta _{3}q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots$$
1050.3.f.c $12$ $28.610$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-10$$ $$q+\beta _{5}q^{2}-\beta _{2}q^{3}+2q^{4}-\beta _{4}q^{6}+(-1+\cdots)q^{7}+\cdots$$
1050.3.f.d $12$ $28.610$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$10$$ $$q-\beta _{5}q^{2}+\beta _{2}q^{3}+2q^{4}-\beta _{4}q^{6}+(1+\cdots)q^{7}+\cdots$$
1050.3.f.e $16$ $28.610$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}-\beta _{1}q^{3}+2q^{4}-\beta _{8}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(1050, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$