Properties

Label 4023.2.a
Level 4023
Weight 2
Character orbit a
Rep. character \(\chi_{4023}(1,\cdot)\)
Character field \(\Q\)
Dimension 198
Newforms 8
Sturm bound 900
Trace bound 2

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Defining parameters

Level: \( N \) = \( 4023 = 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4023.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(900\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4023))\).

Total New Old
Modular forms 456 198 258
Cusp forms 445 198 247
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.

\(3\)\(149\)FrickeDim.
\(+\)\(+\)\(+\)\(43\)
\(+\)\(-\)\(-\)\(57\)
\(-\)\(+\)\(-\)\(56\)
\(-\)\(-\)\(+\)\(42\)
Plus space\(+\)\(85\)
Minus space\(-\)\(113\)

Trace form

\(198q \) \(\mathstrut +\mathstrut 204q^{4} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(198q \) \(\mathstrut +\mathstrut 204q^{4} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 216q^{16} \) \(\mathstrut +\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 214q^{25} \) \(\mathstrut +\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 216q^{49} \) \(\mathstrut +\mathstrut 60q^{52} \) \(\mathstrut +\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 38q^{61} \) \(\mathstrut +\mathstrut 240q^{64} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 84q^{70} \) \(\mathstrut +\mathstrut 18q^{73} \) \(\mathstrut +\mathstrut 48q^{76} \) \(\mathstrut +\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 52q^{82} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 64q^{88} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 149
4023.2.a.a \(18\) \(32.124\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(0\) \(1\) \(-11\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{17}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4023.2.a.b \(18\) \(32.124\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(0\) \(-1\) \(-11\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{17}q^{5}+(-1+\cdots)q^{7}+\cdots\)
4023.2.a.c \(24\) \(32.124\) None \(-7\) \(0\) \(-12\) \(-1\) \(-\) \(-\)
4023.2.a.d \(24\) \(32.124\) None \(7\) \(0\) \(12\) \(-1\) \(-\) \(+\)
4023.2.a.e \(25\) \(32.124\) None \(-7\) \(0\) \(-12\) \(-2\) \(+\) \(+\)
4023.2.a.f \(25\) \(32.124\) None \(7\) \(0\) \(12\) \(-2\) \(+\) \(-\)
4023.2.a.g \(32\) \(32.124\) None \(-1\) \(0\) \(1\) \(13\) \(+\) \(-\)
4023.2.a.h \(32\) \(32.124\) None \(1\) \(0\) \(-1\) \(13\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(447))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1341))\)\(^{\oplus 2}\)