# Properties

 Label 525.2.j Level 525 Weight 2 Character orbit j Rep. character $$\chi_{525}(218,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 72 Newform subspaces 3 Sturm bound 160 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 525.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$160$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(525, [\chi])$$.

Total New Old
Modular forms 184 72 112
Cusp forms 136 72 64
Eisenstein series 48 0 48

## Trace form

 $$72q + 4q^{3} + O(q^{10})$$ $$72q + 4q^{3} - 16q^{12} + 8q^{13} - 88q^{16} + 20q^{18} - 8q^{21} - 8q^{22} + 16q^{27} - 28q^{33} - 32q^{36} + 16q^{37} + 20q^{42} + 40q^{43} + 128q^{46} - 16q^{48} - 80q^{51} - 4q^{57} - 40q^{58} - 64q^{61} + 8q^{63} + 152q^{66} - 24q^{67} + 8q^{72} - 32q^{73} - 64q^{76} - 60q^{78} + 16q^{81} + 80q^{82} - 4q^{87} - 96q^{88} + 48q^{91} + 76q^{93} + 192q^{96} - 24q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
525.2.j.a $$16$$ $$4.192$$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots$$
525.2.j.b $$24$$ $$4.192$$ None $$0$$ $$4$$ $$0$$ $$0$$
525.2.j.c $$32$$ $$4.192$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + T^{4} + 24 T^{8} + 16 T^{12} + 256 T^{16} )^{2}$$)
$3$ ($$1 - 7 T^{4} - 32 T^{8} - 567 T^{12} + 6561 T^{16}$$)
$5$ 1
$7$ ($$( 1 + T^{4} )^{4}$$)
$11$ ($$( 1 + 7 T^{2} + 180 T^{4} + 847 T^{6} + 14641 T^{8} )^{4}$$)
$13$ ($$( 1 - 47 T^{4} + 47568 T^{8} - 1342367 T^{12} + 815730721 T^{16} )^{2}$$)
$17$ ($$( 1 + 193 T^{4} - 1920 T^{8} + 16119553 T^{12} + 6975757441 T^{16} )^{2}$$)
$19$ ($$( 1 - 22 T^{2} + 361 T^{4} )^{8}$$)
$23$ ($$( 1 + 98 T^{4} + 279841 T^{8} )^{4}$$)
$29$ ($$( 1 + 73 T^{2} + 2808 T^{4} + 61393 T^{6} + 707281 T^{8} )^{4}$$)
$31$ ($$( 1 + 2 T + 30 T^{2} + 62 T^{3} + 961 T^{4} )^{8}$$)
$37$ ($$( 1 - 2012 T^{4} + 3915558 T^{8} - 3770811932 T^{12} + 3512479453921 T^{16} )^{2}$$)
$41$ ($$( 1 + 8 T^{2} + 78 T^{4} + 13448 T^{6} + 2825761 T^{8} )^{4}$$)
$43$ ($$( 1 - 3214 T^{4} + 3418801 T^{8} )^{4}$$)
$47$ ($$( 1 - 2087 T^{4} + 6045360 T^{8} - 10183894247 T^{12} + 23811286661761 T^{16} )^{2}$$)
$53$ ($$( 1 - 3836 T^{4} + 14179686 T^{8} - 30267885116 T^{12} + 62259690411361 T^{16} )^{2}$$)
$59$ ($$( 1 + 64 T^{2} + 4686 T^{4} + 222784 T^{6} + 12117361 T^{8} )^{4}$$)
$61$ ($$( 1 - 2 T + 90 T^{2} - 122 T^{3} + 3721 T^{4} )^{8}$$)
$67$ ($$( 1 + 388 T^{4} - 29618010 T^{8} + 7818634948 T^{12} + 406067677556641 T^{16} )^{2}$$)
$71$ ($$( 1 - 208 T^{2} + 19710 T^{4} - 1048528 T^{6} + 25411681 T^{8} )^{4}$$)
$73$ ($$( 1 - 188 T^{4} - 49166394 T^{8} - 5338869308 T^{12} + 806460091894081 T^{16} )^{2}$$)
$79$ ($$( 1 - 83 T^{2} + 1656 T^{4} - 518003 T^{6} + 38950081 T^{8} )^{4}$$)
$83$ ($$( 1 - 9692 T^{4} + 102045030 T^{8} - 459966047132 T^{12} + 2252292232139041 T^{16} )^{2}$$)
$89$ ($$( 1 + 52 T^{2} - 2490 T^{4} + 411892 T^{6} + 62742241 T^{8} )^{4}$$)
$97$ ($$( 1 + 31201 T^{4} + 419298624 T^{8} + 2762202096481 T^{12} + 7837433594376961 T^{16} )^{2}$$)