Properties

Label 2004.2.a
Level $2004$
Weight $2$
Character orbit 2004.a
Rep. character $\chi_{2004}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $4$
Sturm bound $672$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2004.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(672\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2004))\).

Total New Old
Modular forms 342 28 314
Cusp forms 331 28 303
Eisenstein series 11 0 11

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

\(2\)\(3\)\(167\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(9\)
Plus space\(+\)\(10\)
Minus space\(-\)\(18\)

Trace form

\( 28q + 28q^{9} + O(q^{10}) \) \( 28q + 28q^{9} - 4q^{11} + 4q^{13} + 4q^{15} + 16q^{23} + 40q^{25} + 4q^{29} + 8q^{33} - 4q^{35} + 16q^{37} - 8q^{39} + 4q^{41} + 4q^{47} + 20q^{49} + 8q^{53} - 8q^{55} + 8q^{57} - 12q^{59} + 16q^{61} + 36q^{65} + 24q^{67} - 4q^{69} - 12q^{71} - 24q^{73} + 8q^{75} + 16q^{77} - 12q^{79} + 28q^{81} - 8q^{83} + 36q^{85} + 20q^{89} - 16q^{91} + 52q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2004))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 167
2004.2.a.a \(5\) \(16.002\) 5.5.149169.1 None \(0\) \(-5\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2004.2.a.b \(5\) \(16.002\) 5.5.161121.1 None \(0\) \(5\) \(-7\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2004.2.a.c \(9\) \(16.002\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(1\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+q^{9}+\cdots\)
2004.2.a.d \(9\) \(16.002\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(9\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}-\beta _{6}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 2}\)