# Properties

 Label 252.2.n Level 252 Weight 2 Character orbit n Rep. character $$\chi_{252}(31,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 88 Newform subspaces 2 Sturm bound 96 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 252.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$252$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88q + q^{2} + q^{4} - 6q^{6} - 8q^{8} - 2q^{9} + O(q^{10})$$ $$88q + q^{2} + q^{4} - 6q^{6} - 8q^{8} - 2q^{9} - 6q^{10} - 3q^{12} - 15q^{14} + q^{16} - 12q^{17} - 7q^{18} + 24q^{20} - 8q^{21} + 2q^{22} + 6q^{24} - 60q^{25} - 12q^{26} + 26q^{30} + q^{32} - 6q^{33} + 6q^{34} - 38q^{36} - 4q^{37} + 13q^{42} - 5q^{44} - 18q^{45} + 2q^{46} - 9q^{48} - 2q^{49} - 31q^{50} - 4q^{53} - 60q^{54} - 48q^{56} + 12q^{57} + 6q^{58} - 16q^{60} - 6q^{61} - 8q^{64} + 14q^{65} + 15q^{66} + 18q^{69} + 8q^{70} + 17q^{72} - 12q^{73} + 34q^{74} - 12q^{76} + 62q^{77} - 3q^{78} + 51q^{80} + 10q^{81} - 12q^{82} + 29q^{84} - 14q^{85} - 26q^{86} + 14q^{88} - 72q^{89} + 75q^{90} + 44q^{92} - 6q^{93} - 3q^{94} - 54q^{96} - 5q^{98} + O(q^{100})$$

## 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.n.a $$4$$ $$2.012$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\cdots)q^{3}+\cdots$$
252.2.n.b $$84$$ $$2.012$$ None $$-1$$ $$0$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4}$$)
$3$ ($$( 1 - 3 T^{2} )^{2}$$)
$5$ ($$( 1 + 2 T^{2} + 25 T^{4} )^{2}$$)
$7$ ($$1 + 2 T^{2} + 49 T^{4}$$)
$11$ ($$( 1 - 18 T^{2} + 121 T^{4} )^{2}$$)
$13$ ($$( 1 - 7 T + 13 T^{2} )^{2}( 1 - 2 T + 13 T^{2} )^{2}$$)
$17$ ($$( 1 + 9 T + 44 T^{2} + 153 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$1 - 35 T^{2} + 864 T^{4} - 12635 T^{6} + 130321 T^{8}$$)
$23$ ($$( 1 - 30 T^{2} + 529 T^{4} )^{2}$$)
$29$ ($$( 1 + 5 T - 4 T^{2} + 145 T^{3} + 841 T^{4} )^{2}$$)
$31$ ($$1 - 35 T^{2} + 264 T^{4} - 33635 T^{6} + 923521 T^{8}$$)
$37$ ($$( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} )^{2}$$)
$41$ ($$( 1 - 3 T + 44 T^{2} - 123 T^{3} + 1681 T^{4} )^{2}$$)
$43$ ($$1 - 35 T^{2} - 624 T^{4} - 64715 T^{6} + 3418801 T^{8}$$)
$47$ ($$1 - 91 T^{2} + 6072 T^{4} - 201019 T^{6} + 4879681 T^{8}$$)
$53$ ($$( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2}$$)
$59$ ($$1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8}$$)
$61$ ($$( 1 - 9 T + 88 T^{2} - 549 T^{3} + 3721 T^{4} )^{2}$$)
$67$ ($$1 + 53 T^{2} - 1680 T^{4} + 237917 T^{6} + 20151121 T^{8}$$)
$71$ ($$( 1 - 138 T^{2} + 5041 T^{4} )^{2}$$)
$73$ ($$( 1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4} )^{2}$$)
$79$ ($$1 + 149 T^{2} + 15960 T^{4} + 929909 T^{6} + 38950081 T^{8}$$)
$83$ ($$1 - 139 T^{2} + 12432 T^{4} - 957571 T^{6} + 47458321 T^{8}$$)
$89$ ($$( 1 - 15 T + 164 T^{2} - 1335 T^{3} + 7921 T^{4} )^{2}$$)
$97$ ($$( 1 - 3 T + 100 T^{2} - 291 T^{3} + 9409 T^{4} )^{2}$$)