Properties

Label 126.2.k
Level 126
Weight 2
Character orbit k
Rep. character \(\chi_{126}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 8
Newform subspaces 1
Sturm bound 48
Trace bound 0

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 126.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(126, [\chi])\).

Total New Old
Modular forms 64 8 56
Cusp forms 32 8 24
Eisenstein series 32 0 32

Trace form

\( 8q + 4q^{4} + 4q^{7} + O(q^{10}) \) \( 8q + 4q^{4} + 4q^{7} + 12q^{10} - 4q^{16} - 24q^{19} - 24q^{22} - 16q^{25} - 4q^{28} - 12q^{31} - 16q^{37} + 12q^{40} + 32q^{43} + 20q^{49} + 12q^{58} + 24q^{61} - 8q^{64} + 40q^{67} - 12q^{70} + 24q^{73} + 28q^{79} + 48q^{82} - 12q^{88} - 24q^{91} - 24q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
126.2.k.a \(8\) \(1.006\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) \(q+(\zeta_{24}-\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - T^{2} + T^{4} )^{2} \)
$3$ \( \)
$5$ \( ( 1 - 2 T^{2} + 25 T^{4} )^{2}( 1 + 2 T^{2} - 21 T^{4} + 50 T^{6} + 625 T^{8} ) \)
$7$ \( ( 1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4} )^{2} \)
$11$ \( ( 1 + 13 T^{2} + 48 T^{4} + 1573 T^{6} + 14641 T^{8} )^{2} \)
$13$ \( ( 1 - 20 T^{2} + 169 T^{4} )^{4} \)
$17$ \( 1 - 32 T^{2} + 478 T^{4} + 1024 T^{6} - 81341 T^{8} + 295936 T^{10} + 39923038 T^{12} - 772402208 T^{14} + 6975757441 T^{16} \)
$19$ \( ( 1 + 12 T + 92 T^{2} + 528 T^{3} + 2487 T^{4} + 10032 T^{5} + 33212 T^{6} + 82308 T^{7} + 130321 T^{8} )^{2} \)
$23$ \( ( 1 + 28 T^{2} + 255 T^{4} + 14812 T^{6} + 279841 T^{8} )^{2} \)
$29$ \( ( 1 - 62 T^{2} + 1995 T^{4} - 52142 T^{6} + 707281 T^{8} )^{2} \)
$31$ \( ( 1 + 6 T + 23 T^{2} + 66 T^{3} - 468 T^{4} + 2046 T^{5} + 22103 T^{6} + 178746 T^{7} + 923521 T^{8} )^{2} \)
$37$ \( ( 1 + 8 T - 8 T^{2} - 16 T^{3} + 1447 T^{4} - 592 T^{5} - 10952 T^{6} + 405224 T^{7} + 1874161 T^{8} )^{2} \)
$41$ \( ( 1 + 20 T^{2} - 1146 T^{4} + 33620 T^{6} + 2825761 T^{8} )^{2} \)
$43$ \( ( 1 - 8 T + 84 T^{2} - 344 T^{3} + 1849 T^{4} )^{4} \)
$47$ \( 1 - 152 T^{2} + 13198 T^{4} - 834176 T^{6} + 42212419 T^{8} - 1842694784 T^{10} + 64402029838 T^{12} - 1638440730008 T^{14} + 23811286661761 T^{16} \)
$53$ \( 1 + 158 T^{2} + 13753 T^{4} + 883694 T^{6} + 47672164 T^{8} + 2482296446 T^{10} + 108517785193 T^{12} + 3501969058382 T^{14} + 62259690411361 T^{16} \)
$59$ \( 1 - 38 T^{2} - 4727 T^{4} + 30058 T^{6} + 20937316 T^{8} + 104631898 T^{10} - 57278765447 T^{12} - 1602860278358 T^{14} + 146830437604321 T^{16} \)
$61$ \( ( 1 - 12 T + 176 T^{2} - 1536 T^{3} + 15591 T^{4} - 93696 T^{5} + 654896 T^{6} - 2723772 T^{7} + 13845841 T^{8} )^{2} \)
$67$ \( ( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} )^{4} \)
$71$ \( ( 1 - 176 T^{2} + 15234 T^{4} - 887216 T^{6} + 25411681 T^{8} )^{2} \)
$73$ \( ( 1 - 12 T + 182 T^{2} - 1608 T^{3} + 16131 T^{4} - 117384 T^{5} + 969878 T^{6} - 4668204 T^{7} + 28398241 T^{8} )^{2} \)
$79$ \( ( 1 - 14 T + 7 T^{2} - 434 T^{3} + 13996 T^{4} - 34286 T^{5} + 43687 T^{6} - 6902546 T^{7} + 38950081 T^{8} )^{2} \)
$83$ \( ( 1 + 278 T^{2} + 32811 T^{4} + 1915142 T^{6} + 47458321 T^{8} )^{2} \)
$89$ \( ( 1 - 70 T^{2} - 3021 T^{4} - 554470 T^{6} + 62742241 T^{8} )^{2} \)
$97$ \( ( 1 - 190 T^{2} + 20643 T^{4} - 1787710 T^{6} + 88529281 T^{8} )^{2} \)
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