Properties

Label 960.3.j
Level $960$
Weight $3$
Character orbit 960.j
Rep. character $\chi_{960}(319,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $7$
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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(576\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 408 48 360
Cusp forms 360 48 312
Eisenstein series 48 0 48

Trace form

\( 48q + 144q^{9} + O(q^{10}) \) \( 48q + 144q^{9} + 48q^{25} + 160q^{41} + 336q^{49} + 32q^{61} + 96q^{65} + 96q^{69} + 432q^{81} + 288q^{85} + 160q^{89} + O(q^{100}) \)

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.j.a \(4\) \(26.158\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-16\) \(0\) \(q+\zeta_{12}^{2}q^{3}+(-4-\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)
960.3.j.b \(4\) \(26.158\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}-5\zeta_{12}q^{5}-6\zeta_{12}^{3}q^{7}+\cdots\)
960.3.j.c \(4\) \(26.158\) \(\Q(\sqrt{3}, \sqrt{-7})\) None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}-2\beta _{1}q^{7}+3q^{9}+\cdots\)
960.3.j.d \(4\) \(26.158\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(20\) \(0\) \(q-\zeta_{12}q^{3}+5q^{5}-4\zeta_{12}q^{7}+3q^{9}+\cdots\)
960.3.j.e \(8\) \(26.158\) 8.0.\(\cdots\).4 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-3\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
960.3.j.f \(12\) \(26.158\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{6})q^{5}+(\beta _{5}-\beta _{8})q^{7}+\cdots\)
960.3.j.g \(12\) \(26.158\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{8})q^{5}+(-\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)