Properties

Label 960.2.f
Level $960$
Weight $2$
Character orbit 960.f
Rep. character $\chi_{960}(769,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $11$
Sturm bound $384$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).

Total New Old
Modular forms 216 24 192
Cusp forms 168 24 144
Eisenstein series 48 0 48

Trace form

\( 24q - 24q^{9} + O(q^{10}) \) \( 24q - 24q^{9} - 8q^{25} + 16q^{41} - 24q^{49} - 16q^{61} - 16q^{65} + 16q^{69} + 24q^{81} + 48q^{85} + 16q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
960.2.f.a \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots\)
960.2.f.b \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{3}+(-2-i)q^{5}+2iq^{7}-q^{9}+\cdots\)
960.2.f.c \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
960.2.f.d \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
960.2.f.e \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1+2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
960.2.f.f \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
960.2.f.g \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}-6q^{11}+\cdots\)
960.2.f.h \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots\)
960.2.f.i \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots\)
960.2.f.j \(2\) \(7.666\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}+6q^{11}+\cdots\)
960.2.f.k \(4\) \(7.666\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+2\beta _{1}q^{7}-q^{9}+2\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)