Properties

Label 960.2.a
Level $960$
Weight $2$
Character orbit 960.a
Rep. character $\chi_{960}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $16$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(384\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(960))\).

Total New Old
Modular forms 216 16 200
Cusp forms 169 16 153
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(10\)

Trace form

\( 16 q + 16 q^{9} + O(q^{10}) \) \( 16 q + 16 q^{9} - 16 q^{13} - 16 q^{21} + 16 q^{25} + 32 q^{29} + 16 q^{37} + 16 q^{49} + 32 q^{53} + 16 q^{69} + 32 q^{77} + 16 q^{81} + 16 q^{85} - 16 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(960))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
960.2.a.a 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
960.2.a.b 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}+6q^{17}+\cdots\)
960.2.a.c 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
960.2.a.d 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
960.2.a.e 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
960.2.a.f 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
960.2.a.g 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
960.2.a.h 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
960.2.a.i 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
960.2.a.j 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
960.2.a.k 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\)
960.2.a.l 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
960.2.a.m 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
960.2.a.n 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
960.2.a.o 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
960.2.a.p 960.a 1.a $1$ $7.666$ \(\Q\) None \(0\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 2}\)