Properties

Label 4024.2.a
Level $4024$
Weight $2$
Character orbit 4024.a
Rep. character $\chi_{4024}(1,\cdot)$
Character field $\Q$
Dimension $126$
Newform subspaces $7$
Sturm bound $1008$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 4024 = 2^{3} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4024.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(1008\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4024))\).

Total New Old
Modular forms 508 126 382
Cusp forms 501 126 375
Eisenstein series 7 0 7

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

\(2\)\(503\)FrickeDim
\(+\)\(+\)$+$\(29\)
\(+\)\(-\)$-$\(34\)
\(-\)\(+\)$-$\(34\)
\(-\)\(-\)$+$\(29\)
Plus space\(+\)\(58\)
Minus space\(-\)\(68\)

Trace form

\( 126 q - 2 q^{5} + 122 q^{9} + O(q^{10}) \) \( 126 q - 2 q^{5} + 122 q^{9} - 4 q^{11} - 4 q^{17} + 2 q^{19} + 12 q^{23} + 126 q^{25} + 6 q^{29} - 8 q^{31} - 20 q^{33} + 12 q^{35} - 2 q^{37} + 4 q^{39} - 4 q^{41} - 8 q^{43} - 22 q^{45} - 12 q^{47} + 126 q^{49} + 36 q^{51} - 18 q^{53} + 28 q^{55} - 32 q^{57} - 16 q^{59} - 20 q^{61} - 28 q^{63} - 8 q^{65} + 20 q^{67} + 4 q^{69} - 12 q^{73} - 20 q^{75} + 20 q^{77} - 16 q^{79} + 102 q^{81} - 28 q^{83} + 12 q^{85} - 4 q^{87} - 32 q^{91} - 24 q^{93} - 8 q^{95} - 8 q^{97} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 503
4024.2.a.a 4024.a 1.a $1$ $32.132$ \(\Q\) None \(0\) \(-1\) \(0\) \(-5\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-5q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\)
4024.2.a.b 4024.a 1.a $1$ $32.132$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-5q^{11}+3q^{13}+\cdots\)
4024.2.a.c 4024.a 1.a $1$ $32.132$ \(\Q\) None \(0\) \(-1\) \(2\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots\)
4024.2.a.d 4024.a 1.a $28$ $32.132$ None \(0\) \(2\) \(-12\) \(0\) $-$ $-$ $\mathrm{SU}(2)$
4024.2.a.e 4024.a 1.a $29$ $32.132$ None \(0\) \(-7\) \(-4\) \(-13\) $+$ $+$ $\mathrm{SU}(2)$
4024.2.a.f 4024.a 1.a $33$ $32.132$ None \(0\) \(-2\) \(12\) \(4\) $-$ $+$ $\mathrm{SU}(2)$
4024.2.a.g 4024.a 1.a $33$ $32.132$ None \(0\) \(10\) \(0\) \(12\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\)\(^{\oplus 2}\)