Properties

Label 8004.2.a
Level $8004$
Weight $2$
Character orbit 8004.a
Rep. character $\chi_{8004}(1,\cdot)$
Character field $\Q$
Dimension $104$
Newform subspaces $11$
Sturm bound $2880$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8004.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(2880\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8004))\).

Total New Old
Modular forms 1452 104 1348
Cusp forms 1429 104 1325
Eisenstein series 23 0 23

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

\(2\)\(3\)\(23\)\(29\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(14\)
\(-\)\(+\)\(+\)\(-\)$+$\(10\)
\(-\)\(+\)\(-\)\(+\)$+$\(12\)
\(-\)\(+\)\(-\)\(-\)$-$\(16\)
\(-\)\(-\)\(+\)\(+\)$+$\(10\)
\(-\)\(-\)\(+\)\(-\)$-$\(18\)
\(-\)\(-\)\(-\)\(+\)$-$\(16\)
\(-\)\(-\)\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(40\)
Minus space\(-\)\(64\)

Trace form

\( 104 q + 104 q^{9} + O(q^{10}) \) \( 104 q + 104 q^{9} + 8 q^{19} + 8 q^{21} + 112 q^{25} + 8 q^{31} + 8 q^{37} + 16 q^{39} + 8 q^{41} + 16 q^{43} - 8 q^{47} + 120 q^{49} + 32 q^{53} + 8 q^{55} + 8 q^{57} + 16 q^{59} + 16 q^{61} + 56 q^{65} + 32 q^{67} - 8 q^{69} - 8 q^{71} - 8 q^{73} + 24 q^{77} - 16 q^{79} + 104 q^{81} + 72 q^{83} + 24 q^{85} - 16 q^{89} + 8 q^{91} + 24 q^{93} + 32 q^{95} + 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8004))\) 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 23 29
8004.2.a.a 8004.a 1.a $1$ $63.912$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-5\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-5q^{7}+q^{9}-3q^{11}+\cdots\)
8004.2.a.b 8004.a 1.a $1$ $63.912$ \(\Q\) None \(0\) \(-1\) \(-2\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
8004.2.a.c 8004.a 1.a $1$ $63.912$ \(\Q\) None \(0\) \(1\) \(-2\) \(3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
8004.2.a.d 8004.a 1.a $8$ $63.912$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-5\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{7})q^{5}+(\beta _{6}+\beta _{7})q^{7}+\cdots\)
8004.2.a.e 8004.a 1.a $9$ $63.912$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-3\) \(7\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
8004.2.a.f 8004.a 1.a $9$ $63.912$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(-1\) \(-5\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots\)
8004.2.a.g 8004.a 1.a $12$ $63.912$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-3\) \(4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
8004.2.a.h 8004.a 1.a $13$ $63.912$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-13\) \(5\) \(-8\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{12})q^{7}+q^{9}+\cdots\)
8004.2.a.i 8004.a 1.a $16$ $63.912$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-16\) \(5\) \(-4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}-\beta _{12}q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)
8004.2.a.j 8004.a 1.a $16$ $63.912$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(16\) \(3\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots\)
8004.2.a.k 8004.a 1.a $18$ $63.912$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(5\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}-\beta _{9}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4002))\)\(^{\oplus 2}\)