Properties

Label 6044.2.a
Level 6044
Weight 2
Character orbit a
Rep. character \(\chi_{6044}(1,\cdot)\)
Character field \(\Q\)
Dimension 126
Newforms 2
Sturm bound 1512
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6044 = 2^{2} \cdot 1511 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6044.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1512\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6044))\).

Total New Old
Modular forms 759 126 633
Cusp forms 754 126 628
Eisenstein series 5 0 5

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

\(2\)\(1511\)FrickeDim.
\(-\)\(+\)\(-\)\(63\)
\(-\)\(-\)\(+\)\(63\)
Plus space\(+\)\(63\)
Minus space\(-\)\(63\)

Trace form

\(126q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 124q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(126q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 124q^{9} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 120q^{25} \) \(\mathstrut -\mathstrut 20q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 126q^{49} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 8q^{59} \) \(\mathstrut -\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 26q^{65} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 30q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut -\mathstrut 14q^{77} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 102q^{81} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 24q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 22q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6044))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 1511
6044.2.a.a \(63\) \(48.262\) None \(0\) \(-7\) \(-7\) \(-22\) \(-\) \(-\)
6044.2.a.b \(63\) \(48.262\) None \(0\) \(5\) \(5\) \(22\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6044))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1511))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3022))\)\(^{\oplus 2}\)