Properties

Label 768.3.h
Level $768$
Weight $3$
Character orbit 768.h
Rep. character $\chi_{768}(641,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $8$
Sturm bound $384$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(384\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(768, [\chi])\).

Total New Old
Modular forms 280 68 212
Cusp forms 232 60 172
Eisenstein series 48 8 40

Trace form

\( 60q + 4q^{9} + O(q^{10}) \) \( 60q + 4q^{9} + 228q^{25} + 32q^{33} + 308q^{49} + 40q^{57} + 328q^{73} - 4q^{81} + 440q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
768.3.h.a \(2\) \(20.926\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+3iq^{3}-2q^{7}-9q^{9}+22iq^{13}+\cdots\)
768.3.h.b \(2\) \(20.926\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q-3iq^{3}+2q^{7}-9q^{9}+22iq^{13}+\cdots\)
768.3.h.c \(4\) \(20.926\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-24\) \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(\zeta_{8}+2\zeta_{8}^{2})q^{5}+\cdots\)
768.3.h.d \(4\) \(20.926\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(24\) \(q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-2\zeta_{8}^{2})q^{5}+6q^{7}+\cdots\)
768.3.h.e \(8\) \(20.926\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{4})q^{3}+\beta _{7}q^{5}-\beta _{3}q^{7}+\cdots\)
768.3.h.f \(8\) \(20.926\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{3}-\zeta_{24}^{4}q^{5}+(\zeta_{24}^{5}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
768.3.h.g \(16\) \(20.926\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{5}q^{3}-\beta _{9}q^{5}+(-1-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
768.3.h.h \(16\) \(20.926\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(16\) \(q-\beta _{8}q^{3}-\beta _{11}q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)