Properties

Label 24.12.a
Level 24
Weight 12
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 4
Sturm bound 48
Trace bound 5

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 24.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(24))\).

Total New Old
Modular forms 48 5 43
Cusp forms 40 5 35
Eisenstein series 8 0 8

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

\(5q \) \(\mathstrut +\mathstrut 243q^{3} \) \(\mathstrut -\mathstrut 2506q^{5} \) \(\mathstrut -\mathstrut 35592q^{7} \) \(\mathstrut +\mathstrut 295245q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 243q^{3} \) \(\mathstrut -\mathstrut 2506q^{5} \) \(\mathstrut -\mathstrut 35592q^{7} \) \(\mathstrut +\mathstrut 295245q^{9} \) \(\mathstrut +\mathstrut 658244q^{11} \) \(\mathstrut -\mathstrut 2322226q^{13} \) \(\mathstrut +\mathstrut 2277882q^{15} \) \(\mathstrut -\mathstrut 6345542q^{17} \) \(\mathstrut +\mathstrut 33520828q^{19} \) \(\mathstrut -\mathstrut 8135640q^{21} \) \(\mathstrut +\mathstrut 19405352q^{23} \) \(\mathstrut +\mathstrut 38513731q^{25} \) \(\mathstrut +\mathstrut 14348907q^{27} \) \(\mathstrut +\mathstrut 318462366q^{29} \) \(\mathstrut -\mathstrut 251425760q^{31} \) \(\mathstrut +\mathstrut 189241596q^{33} \) \(\mathstrut -\mathstrut 170081136q^{35} \) \(\mathstrut +\mathstrut 394434486q^{37} \) \(\mathstrut -\mathstrut 327729726q^{39} \) \(\mathstrut -\mathstrut 574141278q^{41} \) \(\mathstrut +\mathstrut 519190436q^{43} \) \(\mathstrut -\mathstrut 147976794q^{45} \) \(\mathstrut -\mathstrut 1568688048q^{47} \) \(\mathstrut -\mathstrut 2995248179q^{49} \) \(\mathstrut +\mathstrut 1984229622q^{51} \) \(\mathstrut +\mathstrut 1825434182q^{53} \) \(\mathstrut -\mathstrut 12611903752q^{55} \) \(\mathstrut +\mathstrut 1598958468q^{57} \) \(\mathstrut +\mathstrut 1961805716q^{59} \) \(\mathstrut +\mathstrut 4980362462q^{61} \) \(\mathstrut -\mathstrut 2101672008q^{63} \) \(\mathstrut +\mathstrut 25324822244q^{65} \) \(\mathstrut +\mathstrut 10368215692q^{67} \) \(\mathstrut +\mathstrut 1474051608q^{69} \) \(\mathstrut -\mathstrut 34218445832q^{71} \) \(\mathstrut -\mathstrut 5484242110q^{73} \) \(\mathstrut +\mathstrut 31424816133q^{75} \) \(\mathstrut +\mathstrut 21317107680q^{77} \) \(\mathstrut -\mathstrut 23241508624q^{79} \) \(\mathstrut +\mathstrut 17433922005q^{81} \) \(\mathstrut +\mathstrut 103653834748q^{83} \) \(\mathstrut -\mathstrut 136532770292q^{85} \) \(\mathstrut +\mathstrut 40128430482q^{87} \) \(\mathstrut -\mathstrut 31674497358q^{89} \) \(\mathstrut +\mathstrut 53082773328q^{91} \) \(\mathstrut -\mathstrut 82452878208q^{93} \) \(\mathstrut -\mathstrut 170354909432q^{95} \) \(\mathstrut -\mathstrut 95135791958q^{97} \) \(\mathstrut +\mathstrut 38868649956q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(24))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
24.12.a.a \(1\) \(18.440\) \(\Q\) None \(0\) \(-243\) \(-7130\) \(-19536\) \(+\) \(+\) \(q-3^{5}q^{3}-7130q^{5}-19536q^{7}+3^{10}q^{9}+\cdots\)
24.12.a.b \(1\) \(18.440\) \(\Q\) None \(0\) \(-243\) \(1190\) \(18480\) \(-\) \(+\) \(q-3^{5}q^{3}+1190q^{5}+18480q^{7}+3^{10}q^{9}+\cdots\)
24.12.a.c \(1\) \(18.440\) \(\Q\) None \(0\) \(243\) \(1870\) \(-72312\) \(+\) \(-\) \(q+3^{5}q^{3}+1870q^{5}-72312q^{7}+3^{10}q^{9}+\cdots\)
24.12.a.d \(2\) \(18.440\) \(\Q(\sqrt{3061}) \) None \(0\) \(486\) \(1564\) \(37776\) \(-\) \(-\) \(q+3^{5}q^{3}+(782-\beta )q^{5}+(18888+\beta )q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)