Properties

Label 10.4.b
Level 10
Weight 4
Character orbit b
Rep. character \(\chi_{10}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 6
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 10.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(10, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2q - 8q^{4} - 10q^{5} + 8q^{6} + 46q^{9} + O(q^{10}) \) \( 2q - 8q^{4} - 10q^{5} + 8q^{6} + 46q^{9} + 40q^{10} - 56q^{11} - 104q^{14} - 40q^{15} + 32q^{16} + 120q^{19} + 40q^{20} + 104q^{21} - 32q^{24} - 150q^{25} + 48q^{26} - 180q^{29} - 40q^{30} - 256q^{31} + 256q^{34} + 520q^{35} - 184q^{36} - 48q^{39} - 160q^{40} + 484q^{41} + 224q^{44} - 230q^{45} - 232q^{46} - 666q^{49} - 400q^{50} - 256q^{51} + 400q^{54} + 280q^{55} + 416q^{56} + 40q^{59} + 160q^{60} + 1084q^{61} - 128q^{64} - 240q^{65} - 224q^{66} + 232q^{69} + 520q^{70} - 2256q^{71} - 944q^{74} + 400q^{75} - 480q^{76} + 1440q^{79} - 160q^{80} + 842q^{81} - 416q^{84} - 1280q^{85} + 1448q^{86} + 980q^{89} + 920q^{90} + 624q^{91} - 904q^{94} - 600q^{95} + 128q^{96} - 1288q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
10.4.b.a \(2\) \(0.590\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 4 T^{2} \)
$3$ \( 1 - 50 T^{2} + 729 T^{4} \)
$5$ \( 1 + 10 T + 125 T^{2} \)
$7$ \( 1 - 10 T^{2} + 117649 T^{4} \)
$11$ \( ( 1 + 28 T + 1331 T^{2} )^{2} \)
$13$ \( 1 - 4250 T^{2} + 4826809 T^{4} \)
$17$ \( 1 - 5730 T^{2} + 24137569 T^{4} \)
$19$ \( ( 1 - 60 T + 6859 T^{2} )^{2} \)
$23$ \( 1 - 20970 T^{2} + 148035889 T^{4} \)
$29$ \( ( 1 + 90 T + 24389 T^{2} )^{2} \)
$31$ \( ( 1 + 128 T + 29791 T^{2} )^{2} \)
$37$ \( 1 - 45610 T^{2} + 2565726409 T^{4} \)
$41$ \( ( 1 - 242 T + 68921 T^{2} )^{2} \)
$43$ \( 1 - 27970 T^{2} + 6321363049 T^{4} \)
$47$ \( 1 - 156570 T^{2} + 10779215329 T^{4} \)
$53$ \( 1 - 286090 T^{2} + 22164361129 T^{4} \)
$59$ \( ( 1 - 20 T + 205379 T^{2} )^{2} \)
$61$ \( ( 1 - 542 T + 226981 T^{2} )^{2} \)
$67$ \( 1 - 413170 T^{2} + 90458382169 T^{4} \)
$71$ \( ( 1 + 1128 T + 357911 T^{2} )^{2} \)
$73$ \( 1 - 378610 T^{2} + 151334226289 T^{4} \)
$79$ \( ( 1 - 720 T + 493039 T^{2} )^{2} \)
$83$ \( 1 - 915090 T^{2} + 326940373369 T^{4} \)
$89$ \( ( 1 - 490 T + 704969 T^{2} )^{2} \)
$97$ \( 1 + 294590 T^{2} + 832972004929 T^{4} \)
show more
show less