Properties

Label 960.3.l
Level $960$
Weight $3$
Character orbit 960.l
Rep. character $\chi_{960}(641,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $10$
Sturm bound $576$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(576\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).

Total New Old
Modular forms 408 64 344
Cusp forms 360 64 296
Eisenstein series 48 0 48

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 32 q^{13} - 320 q^{25} + 32 q^{33} - 160 q^{37} + 448 q^{49} - 160 q^{57} + 192 q^{61} + 256 q^{81} + 160 q^{85} + 96 q^{93} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.3.l.a $2$ $26.158$ \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(4\) \(q+(-2-\beta )q^{3}-\beta q^{5}+2q^{7}+(-1+\cdots)q^{9}+\cdots\)
960.3.l.b $2$ $26.158$ \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(12\) \(q+(-2+\beta )q^{3}-\beta q^{5}+6q^{7}+(-1+\cdots)q^{9}+\cdots\)
960.3.l.c $2$ $26.158$ \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(-12\) \(q+(2+\beta )q^{3}+\beta q^{5}-6q^{7}+(-1+4\beta )q^{9}+\cdots\)
960.3.l.d $2$ $26.158$ \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(-4\) \(q+(2+\beta )q^{3}-\beta q^{5}-2q^{7}+(-1+4\beta )q^{9}+\cdots\)
960.3.l.e $4$ $26.158$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(-4\) \(0\) \(8\) \(q+(-1-\beta _{1}+\beta _{2})q^{3}-\beta _{2}q^{5}+(2-5\beta _{1}+\cdots)q^{7}+\cdots\)
960.3.l.f $4$ $26.158$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(4\) \(0\) \(-8\) \(q+(1-\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2-5\beta _{1}+\cdots)q^{7}+\cdots\)
960.3.l.g $8$ $26.158$ 8.0.\(\cdots\).5 None \(0\) \(-4\) \(0\) \(-16\) \(q+\beta _{2}q^{3}-\beta _{6}q^{5}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
960.3.l.h $8$ $26.158$ 8.0.\(\cdots\).5 None \(0\) \(4\) \(0\) \(16\) \(q+\beta _{3}q^{3}+\beta _{4}q^{5}+(3-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
960.3.l.i $16$ $26.158$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{3}+\beta _{5}q^{5}+(-\beta _{8}-\beta _{9})q^{7}+\cdots\)
960.3.l.j $16$ $26.158$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)