# Properties

 Label 2100.2.s Level 2100 Weight 2 Character orbit s Rep. character $$\chi_{2100}(1457,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 72 Newform subspaces 3 Sturm bound 960 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.s (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$960$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2100, [\chi])$$.

Total New Old
Modular forms 1032 72 960
Cusp forms 888 72 816
Eisenstein series 144 0 144

## Trace form

 $$72q + 4q^{3} + O(q^{10})$$ $$72q + 4q^{3} - 24q^{13} - 8q^{21} - 8q^{27} + 32q^{31} + 20q^{33} - 32q^{37} + 8q^{43} + 16q^{51} + 28q^{57} - 8q^{63} + 24q^{67} + 144q^{81} + 20q^{87} + 48q^{91} - 20q^{93} + 104q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2100, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2100.2.s.a $$16$$ $$16.769$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{3}-\beta _{14}q^{7}+(\beta _{7}+\beta _{11})q^{9}+\cdots$$
2100.2.s.b $$24$$ $$16.769$$ None $$0$$ $$4$$ $$0$$ $$0$$
2100.2.s.c $$32$$ $$16.769$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 - 23 T^{4} + 256 T^{8} - 1863 T^{12} + 6561 T^{16}$$)
$5$ 1
$7$ ($$( 1 + T^{4} )^{4}$$)
$11$ ($$( 1 - 29 T^{2} + 448 T^{4} - 3509 T^{6} + 14641 T^{8} )^{4}$$)
$13$ ($$( 1 + 17 T^{4} - 44912 T^{8} + 485537 T^{12} + 815730721 T^{16} )^{2}$$)
$17$ ($$( 1 - 1039 T^{4} + 433824 T^{8} - 86778319 T^{12} + 6975757441 T^{16} )^{2}$$)
$19$ ($$( 1 - 24 T^{2} + 254 T^{4} - 8664 T^{6} + 130321 T^{8} )^{4}$$)
$23$ ($$( 1 + 260 T^{4} + 141382 T^{8} + 72758660 T^{12} + 78310985281 T^{16} )^{2}$$)
$29$ ($$( 1 + T^{2} - 1416 T^{4} + 841 T^{6} + 707281 T^{8} )^{4}$$)
$31$ ($$( 1 - 6 T^{2} + 961 T^{4} )^{8}$$)
$37$ ($$( 1 + 932 T^{4} + 3112486 T^{8} + 1746718052 T^{12} + 3512479453921 T^{16} )^{2}$$)
$41$ ($$( 1 - 104 T^{2} + 5998 T^{4} - 174824 T^{6} + 2825761 T^{8} )^{4}$$)
$43$ ($$( 1 - 4828 T^{4} + 11812006 T^{8} - 16505971228 T^{12} + 11688200277601 T^{16} )^{2}$$)
$47$ ($$( 1 + 6137 T^{4} + 19047856 T^{8} + 29946602297 T^{12} + 23811286661761 T^{16} )^{2}$$)
$53$ ($$( 1 + 740 T^{4} - 5406938 T^{8} + 5838955940 T^{12} + 62259690411361 T^{16} )^{2}$$)
$59$ ($$( 1 + 6350 T^{4} + 12117361 T^{8} )^{4}$$)
$61$ ($$( 1 + 2 T + 106 T^{2} + 122 T^{3} + 3721 T^{4} )^{8}$$)
$67$ ($$( 1 - 2044 T^{4} - 20281946 T^{8} - 41188891324 T^{12} + 406067677556641 T^{16} )^{2}$$)
$71$ ($$( 1 - 84 T^{2} + 2054 T^{4} - 423444 T^{6} + 25411681 T^{8} )^{4}$$)
$73$ ($$( 1 - 96 T^{2} + 5329 T^{4} )^{4}( 1 + 96 T^{2} + 5329 T^{4} )^{4}$$)
$79$ ($$( 1 - 283 T^{2} + 32296 T^{4} - 1766203 T^{6} + 38950081 T^{8} )^{4}$$)
$83$ ($$( 1 + 8420 T^{4} + 39091942 T^{8} + 399599062820 T^{12} + 2252292232139041 T^{16} )^{2}$$)
$89$ ($$( 1 + 116 T^{2} + 18118 T^{4} + 918836 T^{6} + 62742241 T^{8} )^{4}$$)
$97$ ($$( 1 + 32753 T^{4} + 439869408 T^{8} + 2899599540593 T^{12} + 7837433594376961 T^{16} )^{2}$$)