Properties

Label 7524.2.l
Level 7524
Weight 2
Character orbit l
Rep. character \(\chi_{7524}(2089,\cdot)\)
Character field \(\Q\)
Dimension 100
Newforms 6
Sturm bound 2880
Trace bound 25

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Defining parameters

Level: \( N \) = \( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7524.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 209 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(2880\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7524, [\chi])\).

Total New Old
Modular forms 1464 100 1364
Cusp forms 1416 100 1316
Eisenstein series 48 0 48

Trace form

\( 100q + 2q^{5} + O(q^{10}) \) \( 100q + 2q^{5} - q^{11} + 8q^{23} + 106q^{25} - 2q^{47} - 78q^{49} - 5q^{55} + 53q^{77} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7524, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7524.2.l.a \(4\) \(60.079\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(2\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
7524.2.l.b \(8\) \(60.079\) 8.0.\(\cdots\).6 \(\Q(\sqrt{-627}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots\)
7524.2.l.c \(8\) \(60.079\) 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
7524.2.l.d \(16\) \(60.079\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots\)
7524.2.l.e \(24\) \(60.079\) None \(0\) \(0\) \(0\) \(0\)
7524.2.l.f \(40\) \(60.079\) None \(0\) \(0\) \(4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(7524, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7524, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(418, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(627, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1254, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1881, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2508, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3762, [\chi])\)\(^{\oplus 2}\)