Properties

Label 576.3.e
Level $576$
Weight $3$
Character orbit 576.e
Rep. character $\chi_{576}(449,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $8$
Sturm bound $288$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(288\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 216 16 200
Cusp forms 168 16 152
Eisenstein series 48 0 48

Trace form

\( 16 q + O(q^{10}) \) \( 16 q + 32 q^{13} - 80 q^{25} - 160 q^{37} + 112 q^{49} + 160 q^{61} + 320 q^{85} - 64 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.3.e.a \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-24\) \(q+5\beta q^{5}-12q^{7}+4\beta q^{11}+8q^{13}+\cdots\)
576.3.e.b \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-16\) \(q+\beta q^{5}-8q^{7}-8\beta q^{11}+8q^{13}+9\beta q^{17}+\cdots\)
576.3.e.c \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{5}-4q^{7}-4\beta q^{11}-8q^{13}-3\beta q^{17}+\cdots\)
576.3.e.d \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-24q^{13}-23\beta q^{17}+23q^{25}+\cdots\)
576.3.e.e \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+7\beta q^{5}+24q^{13}+7\beta q^{17}-73q^{25}+\cdots\)
576.3.e.f \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(8\) \(q+\beta q^{5}+4q^{7}+4\beta q^{11}-8q^{13}-3\beta q^{17}+\cdots\)
576.3.e.g \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(16\) \(q+\beta q^{5}+8q^{7}+8\beta q^{11}+8q^{13}+9\beta q^{17}+\cdots\)
576.3.e.h \(2\) \(15.695\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(24\) \(q+5\beta q^{5}+12q^{7}-4\beta q^{11}+8q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)