Properties

Label 8004.2.a
Level 8004
Weight 2
Character orbit a
Rep. character \(\chi_{8004}(1,\cdot)\)
Character field \(\Q\)
Dimension 104
Newforms 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: \(\Q\)
Newforms: \( 11 \)
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

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

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

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

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