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Properties

Label 6024.2.a
Level $6024$
Weight $2$
Character orbit 6024.a
Rep. character $\chi_{6024}(1,\cdot)$
Character field $\Q$
Dimension $124$
Newform subspaces $18$
Sturm bound $2016$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 6024 = 2^{3} \cdot 3 \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6024.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(2016\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6024))\).

Total New Old
Modular forms 1016 124 892
Cusp forms 1001 124 877
Eisenstein series 15 0 15

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

\(2\)\(3\)\(251\)FrickeDim
\(+\)\(+\)\(+\)$+$\(15\)
\(+\)\(+\)\(-\)$-$\(16\)
\(+\)\(-\)\(+\)$-$\(20\)
\(+\)\(-\)\(-\)$+$\(12\)
\(-\)\(+\)\(+\)$-$\(14\)
\(-\)\(+\)\(-\)$+$\(16\)
\(-\)\(-\)\(+\)$+$\(13\)
\(-\)\(-\)\(-\)$-$\(18\)
Plus space\(+\)\(56\)
Minus space\(-\)\(68\)

Trace form

\( 124 q + 2 q^{3} + 4 q^{5} + 4 q^{7} + 124 q^{9} + O(q^{10}) \) \( 124 q + 2 q^{3} + 4 q^{5} + 4 q^{7} + 124 q^{9} + 4 q^{13} - 4 q^{17} + 4 q^{19} - 8 q^{23} + 116 q^{25} + 2 q^{27} - 12 q^{29} - 4 q^{31} + 4 q^{39} - 4 q^{41} + 4 q^{43} + 4 q^{45} - 8 q^{47} + 112 q^{49} + 12 q^{51} + 12 q^{53} + 24 q^{55} - 4 q^{57} - 8 q^{59} + 24 q^{61} + 4 q^{63} - 8 q^{65} + 16 q^{67} - 8 q^{69} + 16 q^{71} - 16 q^{73} - 2 q^{75} + 28 q^{79} + 124 q^{81} + 16 q^{83} - 16 q^{85} + 24 q^{87} - 12 q^{89} + 40 q^{91} + 24 q^{93} + 16 q^{95} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6024))\) 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 3 251
6024.2.a.a 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6024.2.a.b 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-3q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6024.2.a.c 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
6024.2.a.d 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6024.2.a.e 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
6024.2.a.f 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
6024.2.a.g 6024.a 1.a $1$ $48.102$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
6024.2.a.h 6024.a 1.a $2$ $48.102$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6024.2.a.i 6024.a 1.a $2$ $48.102$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}-3q^{7}+q^{9}+2q^{11}+\cdots\)
6024.2.a.j 6024.a 1.a $3$ $48.102$ 3.3.148.1 None \(0\) \(3\) \(1\) \(-9\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}-3q^{7}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
6024.2.a.k 6024.a 1.a $8$ $48.102$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-5\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{3}-\beta _{7})q^{7}+\cdots\)
6024.2.a.l 6024.a 1.a $11$ $48.102$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(-11\) \(6\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{3})q^{5}+(\beta _{3}-\beta _{10})q^{7}+\cdots\)
6024.2.a.m 6024.a 1.a $11$ $48.102$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(11\) \(-3\) \(-10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{10})q^{7}+q^{9}+\cdots\)
6024.2.a.n 6024.a 1.a $14$ $48.102$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(-7\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+\cdots\)
6024.2.a.o 6024.a 1.a $14$ $48.102$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(-3\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+(1-\beta _{7})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6024.2.a.p 6024.a 1.a $14$ $48.102$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(6\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}-\beta _{8}q^{11}+\cdots\)
6024.2.a.q 6024.a 1.a $18$ $48.102$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(1\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}-\beta _{14}q^{7}+q^{9}-\beta _{15}q^{11}+\cdots\)
6024.2.a.r 6024.a 1.a $20$ $48.102$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(20\) \(9\) \(9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}-\beta _{13}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3012))\)\(^{\oplus 2}\)