Properties

Label 960.3.c
Level $960$
Weight $3$
Character orbit 960.c
Rep. character $\chi_{960}(449,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $13$
Sturm bound $576$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 960.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(576\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(17\), \(19\)

Dimensions

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

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q - 4 q^{9} + O(q^{10}) \) \( 92 q - 4 q^{9} - 32 q^{21} - 4 q^{25} - 96 q^{45} - 484 q^{49} + 40 q^{61} - 440 q^{69} - 36 q^{81} + 104 q^{85} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.3.c.a 960.c 15.d $1$ $26.158$ \(\Q\) \(\Q(\sqrt{-15}) \) \(0\) \(-3\) \(-5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}-5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots\)
960.3.c.b 960.c 15.d $1$ $26.158$ \(\Q\) \(\Q(\sqrt{-15}) \) \(0\) \(-3\) \(5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+5q^{5}+9q^{9}-15q^{15}+14q^{17}+\cdots\)
960.3.c.c 960.c 15.d $1$ $26.158$ \(\Q\) \(\Q(\sqrt{-15}) \) \(0\) \(3\) \(-5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}-5q^{5}+9q^{9}-15q^{15}-14q^{17}+\cdots\)
960.3.c.d 960.c 15.d $1$ $26.158$ \(\Q\) \(\Q(\sqrt{-15}) \) \(0\) \(3\) \(5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots\)
960.3.c.e 960.c 15.d $4$ $26.158$ \(\Q(\sqrt{2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-2\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
960.3.c.f 960.c 15.d $4$ $26.158$ \(\Q(\sqrt{2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(2\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
960.3.c.g 960.c 15.d $4$ $26.158$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
960.3.c.h 960.c 15.d $4$ $26.158$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
960.3.c.i 960.c 15.d $8$ $26.158$ 8.0.40960000.1 \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{5}q^{3}+5\beta _{1}q^{5}+(2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
960.3.c.j 960.c 15.d $12$ $26.158$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
960.3.c.k 960.c 15.d $12$ $26.158$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
960.3.c.l 960.c 15.d $16$ $26.158$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(\beta _{7}+\beta _{10})q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
960.3.c.m 960.c 15.d $24$ $26.158$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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