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

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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

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