Properties

Label 12.20.b
Level $12$
Weight $20$
Character orbit 12.b
Rep. character $\chi_{12}(11,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 20 \)
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: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(12, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 36 36 0
Eisenstein series 4 4 0

Trace form

\( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} + O(q^{10}) \) \( 36 q - 47880 q^{4} + 21771144 q^{6} - 809473644 q^{9} - 4162950000 q^{10} - 2268767880 q^{12} - 25913431656 q^{13} + 791689296672 q^{16} + 2852271258192 q^{18} - 1650825908424 q^{21} + 7247870602416 q^{22} + 23719435803936 q^{24} - 118879690462380 q^{25} - 7629081673968 q^{28} + 37456727138640 q^{30} + 529254701828640 q^{33} - 248241675948480 q^{34} - 1177548745309416 q^{36} + 1847838600168120 q^{37} - 40433256181440 q^{40} - 2709671988768336 q^{42} - 4365410114088000 q^{45} + 17206125364795104 q^{46} + 1561106052682272 q^{48} - 49399737041580084 q^{49} + 16558671470242896 q^{52} + 40087412948587896 q^{54} + 44803667812766472 q^{57} - 34645536255764880 q^{58} + 50260381053157440 q^{60} + 174742350239997144 q^{61} - 139766490424918656 q^{64} - 87772097712685968 q^{66} - 957190369821780672 q^{69} + 244663962371376480 q^{70} + 54134736422921280 q^{72} - 1445122541399481432 q^{73} + 2744130151937256048 q^{76} + 1125465917961999024 q^{78} + 1033298241353042436 q^{81} + 1064985418859680800 q^{82} + 1920709484261873424 q^{84} - 1802899595088057600 q^{85} - 9209792381828477760 q^{88} - 5194944179528261040 q^{90} + 6719944190337314136 q^{93} - 3835186345170303552 q^{94} - 11947184361208227456 q^{96} + 12765226159947004488 q^{97} + O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.20.b.a 12.b 12.b $36$ $27.458$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$