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Properties

Label 12.22.a
Level $12$
Weight $22$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $44$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 12.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(44\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(12))\).

Total New Old
Modular forms 45 3 42
Cusp forms 39 3 36
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3 q - 59049 q^{3} + 17559810 q^{5} + 791583864 q^{7} + 10460353203 q^{9} + O(q^{10}) \) \( 3 q - 59049 q^{3} + 17559810 q^{5} + 791583864 q^{7} + 10460353203 q^{9} - 112222937772 q^{11} - 1258424621670 q^{13} - 2367628113510 q^{15} + 2953244684214 q^{17} + 25208162419020 q^{19} - 13448739952008 q^{21} + 157775918327784 q^{23} + 435012492283725 q^{25} - 205891132094649 q^{27} - 4359534278069718 q^{29} + 3420045112432992 q^{31} + 2354801655303396 q^{33} + 58943170624401360 q^{35} + 16633045822244802 q^{37} + 21271071576651570 q^{39} - 58021202638110690 q^{41} + 91890557649844404 q^{43} + 61227271592523810 q^{45} + 639021428445851856 q^{47} + 801340454562513867 q^{49} + 76201133615357022 q^{51} - 605389055944970862 q^{53} + 223229472927915960 q^{55} - 2032878440091834180 q^{57} + 111533213628510372 q^{59} - 13790848405425405654 q^{61} + 2760082269078505464 q^{63} - 15411720181369637700 q^{65} + 5308269714319267356 q^{67} + 1914051812556412872 q^{69} + 31114565784489756600 q^{71} - 2692016962386256578 q^{73} - 67005681755538219975 q^{75} + 8172031342996112544 q^{77} - 115367151634837499856 q^{79} + 36472996377170786403 q^{81} + 224057353676040396684 q^{83} + 498730577924263463460 q^{85} - 7791544403279033886 q^{87} + 751807239847095025710 q^{89} - 697445725818940231920 q^{91} - 574631299589364832896 q^{93} + 519788551712918229000 q^{95} - 1581877116210731515482 q^{97} - 391297188857803294572 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(12))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
12.22.a.a 12.a 1.a $1$ $33.537$ \(\Q\) None \(0\) \(59049\) \(-11268090\) \(281914136\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{10}q^{3}-11268090q^{5}+281914136q^{7}+\cdots\)
12.22.a.b 12.a 1.a $2$ $33.537$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-118098\) \(28827900\) \(509669728\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{10}q^{3}+(14413950-5\beta )q^{5}+(254834864+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)