# Properties

 Label 231.2.l Level 231 Weight 2 Character orbit l Rep. character $$\chi_{231}(32,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 56 Newform subspaces 2 Sturm bound 64 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$231 = 3 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 231.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$231$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$64$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(231, [\chi])$$.

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

## Trace form

 $$56q - 2q^{3} - 28q^{4} - 6q^{9} + O(q^{10})$$ $$56q - 2q^{3} - 28q^{4} - 6q^{9} + 6q^{12} - 12q^{15} - 44q^{16} - 24q^{22} - 12q^{25} + 4q^{27} - 22q^{33} + 56q^{34} + 28q^{36} + 96q^{42} + 14q^{45} - 104q^{48} - 4q^{49} - 88q^{55} + 16q^{58} - 48q^{60} + 192q^{64} - 42q^{66} + 20q^{67} - 28q^{69} - 76q^{70} + 46q^{75} + 104q^{78} + 2q^{81} - 4q^{82} - 16q^{88} + 48q^{91} + 48q^{93} - 80q^{97} - 20q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(231, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
231.2.l.a $$8$$ $$1.845$$ 8.0.$$\cdots$$.5 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{4})q^{3}+2\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots$$
231.2.l.b $$48$$ $$1.845$$ None $$0$$ $$-6$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 2 T^{2} + 4 T^{4} )^{4}$$)
$3$ ($$( 1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4} )^{2}$$)
$5$ ($$( 1 + 8 T^{2} + 39 T^{4} + 200 T^{6} + 625 T^{8} )^{2}$$)
$7$ ($$( 1 + 7 T^{2} + 49 T^{4} )^{2}$$)
$11$ ($$1 + 20 T^{2} + 279 T^{4} + 2420 T^{6} + 14641 T^{8}$$)
$13$ ($$( 1 - 5 T^{2} + 169 T^{4} )^{4}$$)
$17$ ($$( 1 + 8 T^{2} - 225 T^{4} + 2312 T^{6} + 83521 T^{8} )^{2}$$)
$19$ ($$( 1 + 17 T^{2} - 72 T^{4} + 6137 T^{6} + 130321 T^{8} )^{2}$$)
$23$ ($$( 1 + 14 T^{2} - 333 T^{4} + 7406 T^{6} + 279841 T^{8} )^{2}$$)
$29$ ($$( 1 + 16 T^{2} + 841 T^{4} )^{4}$$)
$31$ ($$( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} )^{4}$$)
$37$ ($$( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} )^{4}$$)
$41$ ($$( 1 + 40 T^{2} + 1681 T^{4} )^{4}$$)
$43$ ($$( 1 - 65 T^{2} + 1849 T^{4} )^{4}$$)
$47$ ($$( 1 + 62 T^{2} + 1635 T^{4} + 136958 T^{6} + 4879681 T^{8} )^{2}$$)
$53$ ($$( 1 + 56 T^{2} + 327 T^{4} + 157304 T^{6} + 7890481 T^{8} )^{2}$$)
$59$ ($$( 1 + 110 T^{2} + 8619 T^{4} + 382910 T^{6} + 12117361 T^{8} )^{2}$$)
$61$ ($$( 1 + 61 T^{2} + 3721 T^{4} )^{4}$$)
$67$ ($$( 1 - T - 66 T^{2} - 67 T^{3} + 4489 T^{4} )^{4}$$)
$71$ ($$( 1 - 140 T^{2} + 5041 T^{4} )^{4}$$)
$73$ ($$( 1 + 125 T^{2} + 10296 T^{4} + 666125 T^{6} + 28398241 T^{8} )^{2}$$)
$79$ ($$( 1 - 31 T^{2} - 5280 T^{4} - 193471 T^{6} + 38950081 T^{8} )^{2}$$)
$83$ ($$( 1 + 124 T^{2} + 6889 T^{4} )^{4}$$)
$89$ ($$( 1 - 64 T^{2} - 3825 T^{4} - 506944 T^{6} + 62742241 T^{8} )^{2}$$)
$97$ ($$( 1 - 8 T + 97 T^{2} )^{8}$$)