Properties

Label 4024.2.a
Level 4024
Weight 2
Character orbit a
Rep. character \(\chi_{4024}(1,\cdot)\)
Character field \(\Q\)
Dimension 126
Newforms 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: \(\Q\)
Newforms: \( 7 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 503
4024.2.a.a \(1\) \(32.132\) \(\Q\) None \(0\) \(-1\) \(0\) \(-5\) \(-\) \(+\) \(q-q^{3}-5q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\)
4024.2.a.b \(1\) \(32.132\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(-\) \(q-q^{3}+q^{7}-2q^{9}-5q^{11}+3q^{13}+\cdots\)
4024.2.a.c \(1\) \(32.132\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots\)
4024.2.a.d \(28\) \(32.132\) None \(0\) \(2\) \(-12\) \(0\) \(-\) \(-\)
4024.2.a.e \(29\) \(32.132\) None \(0\) \(-7\) \(-4\) \(-13\) \(+\) \(+\)
4024.2.a.f \(33\) \(32.132\) None \(0\) \(-2\) \(12\) \(4\) \(-\) \(+\)
4024.2.a.g \(33\) \(32.132\) None \(0\) \(10\) \(0\) \(12\) \(+\) \(-\)

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

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