Properties

Label 24.10.a
Level 24
Weight 10
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 4
Sturm bound 40
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 24.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(24))\).

Total New Old
Modular forms 40 5 35
Cusp forms 32 5 27
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut -\mathstrut 81q^{3} \) \(\mathstrut -\mathstrut 122q^{5} \) \(\mathstrut -\mathstrut 5904q^{7} \) \(\mathstrut +\mathstrut 32805q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 81q^{3} \) \(\mathstrut -\mathstrut 122q^{5} \) \(\mathstrut -\mathstrut 5904q^{7} \) \(\mathstrut +\mathstrut 32805q^{9} \) \(\mathstrut -\mathstrut 56924q^{11} \) \(\mathstrut +\mathstrut 253814q^{13} \) \(\mathstrut -\mathstrut 19278q^{15} \) \(\mathstrut +\mathstrut 371690q^{17} \) \(\mathstrut +\mathstrut 166300q^{19} \) \(\mathstrut -\mathstrut 120528q^{21} \) \(\mathstrut +\mathstrut 2393560q^{23} \) \(\mathstrut +\mathstrut 265051q^{25} \) \(\mathstrut -\mathstrut 531441q^{27} \) \(\mathstrut -\mathstrut 736818q^{29} \) \(\mathstrut +\mathstrut 56248q^{31} \) \(\mathstrut +\mathstrut 446796q^{33} \) \(\mathstrut -\mathstrut 32502624q^{35} \) \(\mathstrut +\mathstrut 21407934q^{37} \) \(\mathstrut -\mathstrut 11710494q^{39} \) \(\mathstrut +\mathstrut 3652674q^{41} \) \(\mathstrut -\mathstrut 38861212q^{43} \) \(\mathstrut -\mathstrut 800442q^{45} \) \(\mathstrut +\mathstrut 77893536q^{47} \) \(\mathstrut +\mathstrut 43083805q^{49} \) \(\mathstrut -\mathstrut 62200386q^{51} \) \(\mathstrut -\mathstrut 122788058q^{53} \) \(\mathstrut +\mathstrut 191168888q^{55} \) \(\mathstrut +\mathstrut 12974580q^{57} \) \(\mathstrut +\mathstrut 35469124q^{59} \) \(\mathstrut +\mathstrut 203888918q^{61} \) \(\mathstrut -\mathstrut 38736144q^{63} \) \(\mathstrut -\mathstrut 197295884q^{65} \) \(\mathstrut -\mathstrut 183464900q^{67} \) \(\mathstrut +\mathstrut 163576584q^{69} \) \(\mathstrut +\mathstrut 334361960q^{71} \) \(\mathstrut +\mathstrut 307233266q^{73} \) \(\mathstrut -\mathstrut 491077647q^{75} \) \(\mathstrut -\mathstrut 1124684736q^{77} \) \(\mathstrut -\mathstrut 598882456q^{79} \) \(\mathstrut +\mathstrut 215233605q^{81} \) \(\mathstrut +\mathstrut 1832558108q^{83} \) \(\mathstrut -\mathstrut 291062708q^{85} \) \(\mathstrut -\mathstrut 837938358q^{87} \) \(\mathstrut -\mathstrut 1995331614q^{89} \) \(\mathstrut +\mathstrut 192513312q^{91} \) \(\mathstrut +\mathstrut 1493236296q^{93} \) \(\mathstrut +\mathstrut 2022308360q^{95} \) \(\mathstrut +\mathstrut 1970064970q^{97} \) \(\mathstrut -\mathstrut 373478364q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.10.a.a \(1\) \(12.361\) \(\Q\) None \(0\) \(-81\) \(830\) \(672\) \(+\) \(+\) \(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.b \(1\) \(12.361\) \(\Q\) None \(0\) \(81\) \(-794\) \(-5880\) \(-\) \(-\) \(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.c \(1\) \(12.361\) \(\Q\) None \(0\) \(81\) \(614\) \(2184\) \(+\) \(-\) \(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.d \(2\) \(12.361\) \(\Q(\sqrt{109}) \) None \(0\) \(-162\) \(-772\) \(-2880\) \(-\) \(+\) \(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)