Properties

Label 6044.2.a
Level 6044
Weight 2
Character orbit a
Rep. character \(\chi_{6044}(1,\cdot)\)
Character field \(\Q\)
Dimension 126
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6044))\) into newform subspaces

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database