Properties

Label 12.4.b
Level 12
Weight 4
Character orbit b
Rep. character \(\chi_{12}(11,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(12, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 8q^{4} - 24q^{6} - 12q^{9} + O(q^{10}) \) \( 4q - 8q^{4} - 24q^{6} - 12q^{9} + 80q^{10} + 120q^{12} - 40q^{13} - 224q^{16} - 240q^{18} + 120q^{21} + 240q^{22} + 288q^{24} + 180q^{25} - 240q^{28} - 240q^{30} - 480q^{33} + 320q^{34} + 24q^{36} - 520q^{37} + 320q^{40} + 240q^{42} + 960q^{45} - 672q^{46} - 480q^{48} + 1132q^{49} + 80q^{52} + 792q^{54} - 1080q^{57} - 1360q^{58} - 960q^{60} - 1768q^{61} + 1408q^{64} + 1200q^{66} + 1344q^{69} + 480q^{70} - 960q^{72} + 1640q^{73} + 2160q^{76} + 240q^{78} - 2844q^{81} - 1120q^{82} - 240q^{84} - 1280q^{85} - 2880q^{88} - 240q^{90} + 3480q^{93} - 1344q^{94} + 384q^{96} + 3080q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.4.b.a \(4\) \(0.708\) \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 4 T^{2} + 64 T^{4} \)
$3$ \( 1 + 6 T^{2} + 729 T^{4} \)
$5$ \( ( 1 - 170 T^{2} + 15625 T^{4} )^{2} \)
$7$ \( ( 1 - 626 T^{2} + 117649 T^{4} )^{2} \)
$11$ \( ( 1 + 1462 T^{2} + 1771561 T^{4} )^{2} \)
$13$ \( ( 1 + 10 T + 2197 T^{2} )^{4} \)
$17$ \( ( 1 - 8546 T^{2} + 24137569 T^{4} )^{2} \)
$19$ \( ( 1 - 8858 T^{2} + 47045881 T^{4} )^{2} \)
$23$ \( ( 1 + 14926 T^{2} + 148035889 T^{4} )^{2} \)
$29$ \( ( 1 - 25658 T^{2} + 594823321 T^{4} )^{2} \)
$31$ \( ( 1 - 9122 T^{2} + 887503681 T^{4} )^{2} \)
$37$ \( ( 1 + 130 T + 50653 T^{2} )^{4} \)
$41$ \( ( 1 - 122162 T^{2} + 4750104241 T^{4} )^{2} \)
$43$ \( ( 1 - 108554 T^{2} + 6321363049 T^{4} )^{2} \)
$47$ \( ( 1 + 170014 T^{2} + 10779215329 T^{4} )^{2} \)
$53$ \( ( 1 - 74 T^{2} + 22164361129 T^{4} )^{2} \)
$59$ \( ( 1 + 380758 T^{2} + 42180533641 T^{4} )^{2} \)
$61$ \( ( 1 + 442 T + 226981 T^{2} )^{4} \)
$67$ \( ( 1 - 60026 T^{2} + 90458382169 T^{4} )^{2} \)
$71$ \( ( 1 - 364178 T^{2} + 128100283921 T^{4} )^{2} \)
$73$ \( ( 1 - 410 T + 389017 T^{2} )^{4} \)
$79$ \( ( 1 - 978818 T^{2} + 243087455521 T^{4} )^{2} \)
$83$ \( ( 1 - 428954 T^{2} + 326940373369 T^{4} )^{2} \)
$89$ \( ( 1 - 703058 T^{2} + 496981290961 T^{4} )^{2} \)
$97$ \( ( 1 - 770 T + 912673 T^{2} )^{4} \)
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