# Properties

 Label 3150.2.k Level 3150 Weight 2 Character orbit k Rep. character $$\chi_{3150}(1801,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 128 Sturm bound 1440

# Related objects

## Defining parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.k (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$7$$ Character field: $$\Q(\zeta_{3})$$ Sturm bound: $$1440$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3150, [\chi])$$.

Total New Old
Modular forms 1536 128 1408
Cusp forms 1344 128 1216
Eisenstein series 192 0 192

## Trace form

 $$128q$$ $$\mathstrut -\mathstrut 64q^{4}$$ $$\mathstrut +\mathstrut 4q^{7}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$128q$$ $$\mathstrut -\mathstrut 64q^{4}$$ $$\mathstrut +\mathstrut 4q^{7}$$ $$\mathstrut -\mathstrut 8q^{11}$$ $$\mathstrut +\mathstrut 4q^{14}$$ $$\mathstrut -\mathstrut 64q^{16}$$ $$\mathstrut +\mathstrut 16q^{17}$$ $$\mathstrut -\mathstrut 12q^{19}$$ $$\mathstrut -\mathstrut 8q^{23}$$ $$\mathstrut -\mathstrut 12q^{26}$$ $$\mathstrut -\mathstrut 8q^{28}$$ $$\mathstrut +\mathstrut 16q^{31}$$ $$\mathstrut -\mathstrut 4q^{37}$$ $$\mathstrut +\mathstrut 4q^{38}$$ $$\mathstrut +\mathstrut 24q^{41}$$ $$\mathstrut -\mathstrut 24q^{43}$$ $$\mathstrut -\mathstrut 8q^{44}$$ $$\mathstrut -\mathstrut 8q^{46}$$ $$\mathstrut +\mathstrut 8q^{47}$$ $$\mathstrut +\mathstrut 20q^{49}$$ $$\mathstrut +\mathstrut 32q^{53}$$ $$\mathstrut -\mathstrut 8q^{56}$$ $$\mathstrut +\mathstrut 4q^{58}$$ $$\mathstrut -\mathstrut 28q^{59}$$ $$\mathstrut -\mathstrut 16q^{61}$$ $$\mathstrut -\mathstrut 8q^{62}$$ $$\mathstrut +\mathstrut 128q^{64}$$ $$\mathstrut +\mathstrut 40q^{67}$$ $$\mathstrut +\mathstrut 16q^{68}$$ $$\mathstrut -\mathstrut 32q^{71}$$ $$\mathstrut -\mathstrut 12q^{73}$$ $$\mathstrut +\mathstrut 8q^{74}$$ $$\mathstrut +\mathstrut 24q^{76}$$ $$\mathstrut -\mathstrut 60q^{77}$$ $$\mathstrut +\mathstrut 32q^{79}$$ $$\mathstrut +\mathstrut 16q^{82}$$ $$\mathstrut -\mathstrut 48q^{83}$$ $$\mathstrut +\mathstrut 12q^{86}$$ $$\mathstrut -\mathstrut 8q^{89}$$ $$\mathstrut -\mathstrut 36q^{91}$$ $$\mathstrut +\mathstrut 16q^{92}$$ $$\mathstrut +\mathstrut 28q^{94}$$ $$\mathstrut +\mathstrut 72q^{97}$$ $$\mathstrut +\mathstrut 48q^{98}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3150, [\chi])$$ into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(3150, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$