# Properties

 Label 252.2.e Level 252 Weight 2 Character orbit e Rep. character $$\chi_{252}(71,\cdot)$$ Character field $$\Q$$ Dimension 12 Newform subspaces 1 Sturm bound 96 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 252.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$12$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(252, [\chi])$$.

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

## Trace form

 $$12q + 8q^{4} + O(q^{10})$$ $$12q + 8q^{4} - 8q^{10} - 20q^{16} + 20q^{22} - 12q^{25} - 4q^{28} - 16q^{34} + 8q^{37} + 8q^{40} - 36q^{46} - 12q^{49} - 16q^{52} + 4q^{58} + 56q^{61} - 16q^{64} + 24q^{70} + 72q^{76} + 56q^{82} - 56q^{85} + 28q^{88} - 24q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(252, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
252.2.e.a $$12$$ $$2.012$$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(252, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(252, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ $$1 - 4 T^{2} + 13 T^{4} - 28 T^{6} + 52 T^{8} - 64 T^{10} + 64 T^{12}$$
$3$ 
$5$ $$( 1 - 12 T^{2} + 95 T^{4} - 568 T^{6} + 2375 T^{8} - 7500 T^{10} + 15625 T^{12} )^{2}$$
$7$ $$( 1 + T^{2} )^{6}$$
$11$ $$( 1 + 38 T^{2} + 715 T^{4} + 9068 T^{6} + 86515 T^{8} + 556358 T^{10} + 1771561 T^{12} )^{2}$$
$13$ $$( 1 + 11 T^{2} - 16 T^{3} + 143 T^{4} + 2197 T^{6} )^{4}$$
$17$ $$( 1 - 68 T^{2} + 2167 T^{4} - 44168 T^{6} + 626263 T^{8} - 5679428 T^{10} + 24137569 T^{12} )^{2}$$
$19$ $$( 1 - 50 T^{2} + 1639 T^{4} - 35804 T^{6} + 591679 T^{8} - 6516050 T^{10} + 47045881 T^{12} )^{2}$$
$23$ $$( 1 - 2 T^{2} + 979 T^{4} + 3772 T^{6} + 517891 T^{8} - 559682 T^{10} + 148035889 T^{12} )^{2}$$
$29$ $$( 1 - 56 T^{2} + 841 T^{4} )^{6}$$
$31$ $$( 1 - 58 T^{2} + 3727 T^{4} - 113644 T^{6} + 3581647 T^{8} - 53564218 T^{10} + 887503681 T^{12} )^{2}$$
$37$ $$( 1 - 2 T + 47 T^{2} - 276 T^{3} + 1739 T^{4} - 2738 T^{5} + 50653 T^{6} )^{4}$$
$41$ $$( 1 - 132 T^{2} + 10823 T^{4} - 527752 T^{6} + 18193463 T^{8} - 373000452 T^{10} + 4750104241 T^{12} )^{2}$$
$43$ $$( 1 - 98 T^{2} + 4567 T^{4} - 172988 T^{6} + 8444383 T^{8} - 335042498 T^{10} + 6321363049 T^{12} )^{2}$$
$47$ $$( 1 + 10 T^{2} + 4591 T^{4} + 70732 T^{6} + 10141519 T^{8} + 48796810 T^{10} + 10779215329 T^{12} )^{2}$$
$53$ $$( 1 - 184 T^{2} + 16171 T^{4} - 975856 T^{6} + 45424339 T^{8} - 1451848504 T^{10} + 22164361129 T^{12} )^{2}$$
$59$ $$( 1 + 146 T^{2} + 7799 T^{4} + 306396 T^{6} + 27148319 T^{8} + 1769134706 T^{10} + 42180533641 T^{12} )^{2}$$
$61$ $$( 1 - 14 T + 187 T^{2} - 1700 T^{3} + 11407 T^{4} - 52094 T^{5} + 226981 T^{6} )^{4}$$
$67$ $$( 1 - 186 T^{2} + 13175 T^{4} - 680684 T^{6} + 59142575 T^{8} - 3748108506 T^{10} + 90458382169 T^{12} )^{2}$$
$71$ $$( 1 + 158 T^{2} + 5683 T^{4} - 107140 T^{6} + 28648003 T^{8} + 4015045598 T^{10} + 128100283921 T^{12} )^{2}$$
$73$ $$( 1 + 47 T^{2} - 352 T^{3} + 3431 T^{4} + 389017 T^{6} )^{4}$$
$79$ $$( 1 - 162 T^{2} + 19359 T^{4} - 2006332 T^{6} + 120819519 T^{8} - 6309913122 T^{10} + 243087455521 T^{12} )^{2}$$
$83$ $$( 1 + 370 T^{2} + 65191 T^{4} + 6834652 T^{6} + 449100799 T^{8} + 17559578770 T^{10} + 326940373369 T^{12} )^{2}$$
$89$ $$( 1 - 308 T^{2} + 49895 T^{4} - 5241384 T^{6} + 395218295 T^{8} - 19324610228 T^{10} + 496981290961 T^{12} )^{2}$$
$97$ $$( 1 + 135 T^{2} + 128 T^{3} + 13095 T^{4} + 912673 T^{6} )^{4}$$