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Properties

Label 6.24.a
Level $6$
Weight $24$
Character orbit 6.a
Rep. character $\chi_{6}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(6))\).

Total New Old
Modular forms 25 5 20
Cusp forms 21 5 16
Eisenstein series 4 0 4

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

Trace form

\( 5 q + 2048 q^{2} + 177147 q^{3} + 20971520 q^{4} + 176996406 q^{5} + 362797056 q^{6} - 4237234616 q^{7} + 8589934592 q^{8} + 156905298045 q^{9} + O(q^{10}) \) \( 5 q + 2048 q^{2} + 177147 q^{3} + 20971520 q^{4} + 176996406 q^{5} + 362797056 q^{6} - 4237234616 q^{7} + 8589934592 q^{8} + 156905298045 q^{9} - 296017170432 q^{10} + 1003123321476 q^{11} + 743008370688 q^{12} - 7163026465442 q^{13} + 34399692832768 q^{14} - 34980614727318 q^{15} + 87960930222080 q^{16} - 112782974472486 q^{17} + 64268410079232 q^{18} - 310280498618372 q^{19} + 742376733671424 q^{20} + 1947636372312216 q^{21} - 1390815609544704 q^{22} + 1091508779588808 q^{23} + 1521681143169024 q^{24} + 50260527743649011 q^{25} - 8027709273853952 q^{26} + 5559060566555523 q^{27} - 17772250098827264 q^{28} - 99961439759178978 q^{29} + 96504904297598976 q^{30} + 35287126783634992 q^{31} + 36028797018963968 q^{32} + 334239245081343324 q^{33} + 451969640981434368 q^{34} - 3185250515442176016 q^{35} + 658108519211335680 q^{36} + 2184681535330439494 q^{37} - 2955461424926105600 q^{38} + 3769789175671448034 q^{39} - 1241586002011619328 q^{40} - 7175024896070871006 q^{41} - 179984945867636736 q^{42} - 5097358113597481052 q^{43} + 4207404159760072704 q^{44} + 5554334767264765254 q^{45} + 35007774422183657472 q^{46} - 14229378350010956496 q^{47} + 3116402981210161152 q^{48} - 4598966682961731219 q^{49} + 37677055077602736128 q^{50} - 34320604362729874074 q^{51} - 30043910556109242368 q^{52} + 234223356751179775398 q^{53} + 11384956040305711104 q^{54} - 335154261360461265288 q^{55} + 144282769247250153472 q^{56} - 200706972704273943900 q^{57} - 299100993176550789120 q^{58} + 152508933846181136820 q^{59} - 146719332273248796672 q^{60} - 4138430899733804594 q^{61} + 231191008877334102016 q^{62} - 132968912062014225144 q^{63} + 368934881474191032320 q^{64} - 122198805828402197052 q^{65} + 673961350697387974656 q^{66} - 1768116382254855109076 q^{67} - 473046080961845919744 q^{68} + 3707400720892013383608 q^{69} - 333979373351091929088 q^{70} - 2194690514921335050984 q^{71} + 269561249468963094528 q^{72} + 5952999331900670778658 q^{73} - 6899046201622854471680 q^{74} + 3676227016437321643917 q^{75} - 1301410736477032153088 q^{76} + 8650595650759554766368 q^{77} + 298683737090239500288 q^{78} - 8727974492151704609216 q^{79} + 3113753703544988368896 q^{80} + 4923854510918056164405 q^{81} - 6953851231654721040384 q^{82} - 7399120770700019764932 q^{83} + 8168979026934616817664 q^{84} - 38780668013169670874676 q^{85} + 17633077782559449948160 q^{86} - 34206403589500341438270 q^{87} - 5833503474375790166016 q^{88} + 30781916884140576690834 q^{89} - 9289332470614104281088 q^{90} + 14484144161662588345520 q^{91} + 4578119640264455749632 q^{92} - 40848521962015013121936 q^{93} - 13406598768185929334784 q^{94} + 275170814179738588373640 q^{95} + 6382393305518410039296 q^{96} - 165669030098805755912726 q^{97} - 79337738079274835490816 q^{98} + 31479072746416425862884 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(6))\) 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
6.24.a.a 6.a 1.a $1$ $20.112$ \(\Q\) None \(-2048\) \(-177147\) \(196251270\) \(-8131131904\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}+196251270q^{5}+\cdots\)
6.24.a.b 6.a 1.a $1$ $20.112$ \(\Q\) None \(-2048\) \(177147\) \(-35483250\) \(-2385847912\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}-35483250q^{5}+\cdots\)
6.24.a.c 6.a 1.a $1$ $20.112$ \(\Q\) None \(2048\) \(-177147\) \(-9019770\) \(515282432\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}-9019770q^{5}+\cdots\)
6.24.a.d 6.a 1.a $2$ $20.112$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(4096\) \(354294\) \(25248156\) \(5764462768\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}+(12624078+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(6))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)