Properties

Label 1575.2.g
Level 1575
Weight 2
Character orbit g
Rep. character \(\chi_{1575}(1574,\cdot)\)
Character field \(\Q\)
Dimension 48
Newforms 5
Sturm bound 480
Trace bound 14

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(59\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 264 48 216
Cusp forms 216 48 168
Eisenstein series 48 0 48

Trace form

\(48q \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48q \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 96q^{46} \) \(\mathstrut -\mathstrut 36q^{49} \) \(\mathstrut +\mathstrut 192q^{64} \) \(\mathstrut -\mathstrut 48q^{79} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1575.2.g.a \(8\) \(12.576\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}+\zeta_{24}^{3}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
1575.2.g.b \(8\) \(12.576\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{6}q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{7}-2\zeta_{24}^{6}q^{8}+\cdots\)
1575.2.g.c \(8\) \(12.576\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}+\zeta_{24}^{3}q^{4}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
1575.2.g.d \(8\) \(12.576\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(2+\beta _{5})q^{4}-\beta _{1}q^{7}+(\beta _{3}+\cdots)q^{8}+\cdots\)
1575.2.g.e \(16\) \(12.576\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{10}q^{2}+(2+\beta _{4})q^{4}-\beta _{9}q^{7}+(\beta _{3}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)