Properties

Label 960.4.a
Level $960$
Weight $4$
Character orbit 960.a
Rep. character $\chi_{960}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $42$
Sturm bound $768$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(768\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(960))\).

Total New Old
Modular forms 600 48 552
Cusp forms 552 48 504
Eisenstein series 48 0 48

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.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(26\)
Minus space\(-\)\(22\)

Trace form

\( 48 q + 432 q^{9} + O(q^{10}) \) \( 48 q + 432 q^{9} + 144 q^{13} - 240 q^{21} + 1200 q^{25} - 800 q^{29} - 1040 q^{37} + 2352 q^{49} + 1504 q^{53} - 3072 q^{61} - 528 q^{69} + 3808 q^{77} + 3888 q^{81} + 240 q^{85} - 3696 q^{93} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(960))\) 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
960.4.a.a 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(-32\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}-2^{5}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
960.4.a.b 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(-24\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}-24q^{7}+9q^{9}-52q^{11}+\cdots\)
960.4.a.c 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(-16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}-2^{4}q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.d 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}-12q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.e 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+9q^{9}+4q^{11}-54q^{13}+\cdots\)
960.4.a.f 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+4q^{7}+9q^{9}+40q^{11}+\cdots\)
960.4.a.g 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+8q^{7}+9q^{9}-20q^{11}+\cdots\)
960.4.a.h 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+2^{4}q^{7}+9q^{9}-28q^{11}+\cdots\)
960.4.a.i 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(32\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+2^{5}q^{7}+9q^{9}-2^{6}q^{11}+\cdots\)
960.4.a.j 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(-5\) \(32\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+2^{5}q^{7}+9q^{9}+60q^{11}+\cdots\)
960.4.a.k 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(-20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}-20q^{7}+9q^{9}-56q^{11}+\cdots\)
960.4.a.l 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(-20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}-20q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.m 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}-8q^{7}+9q^{9}-4q^{11}+\cdots\)
960.4.a.n 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}-4q^{7}+9q^{9}+48q^{11}+\cdots\)
960.4.a.o 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}-4q^{7}+9q^{9}+72q^{11}+\cdots\)
960.4.a.p 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+12q^{7}+9q^{9}+20q^{11}+\cdots\)
960.4.a.q 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(20\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+20q^{7}+9q^{9}-2^{4}q^{11}+\cdots\)
960.4.a.r 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(-3\) \(5\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+28q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.s 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(-32\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}-2^{5}q^{7}+9q^{9}-60q^{11}+\cdots\)
960.4.a.t 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(-32\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}-2^{5}q^{7}+9q^{9}+2^{6}q^{11}+\cdots\)
960.4.a.u 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(-16\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}-2^{4}q^{7}+9q^{9}+28q^{11}+\cdots\)
960.4.a.v 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}-8q^{7}+9q^{9}+20q^{11}+\cdots\)
960.4.a.w 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}-4q^{7}+9q^{9}-40q^{11}+\cdots\)
960.4.a.x 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+9q^{9}-4q^{11}-54q^{13}+\cdots\)
960.4.a.y 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+12q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.z 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(16\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+2^{4}q^{7}+9q^{9}-24q^{11}+\cdots\)
960.4.a.ba 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(24\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+24q^{7}+9q^{9}+52q^{11}+\cdots\)
960.4.a.bb 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(-5\) \(32\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+2^{5}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
960.4.a.bc 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(-28\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}-28q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.bd 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(-20\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}-20q^{7}+9q^{9}+2^{4}q^{11}+\cdots\)
960.4.a.be 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(-12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}-12q^{7}+9q^{9}-20q^{11}+\cdots\)
960.4.a.bf 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+4q^{7}+9q^{9}-72q^{11}+\cdots\)
960.4.a.bg 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+4q^{7}+9q^{9}-48q^{11}+\cdots\)
960.4.a.bh 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+8q^{7}+9q^{9}+4q^{11}+\cdots\)
960.4.a.bi 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(20\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+20q^{7}+9q^{9}+24q^{11}+\cdots\)
960.4.a.bj 960.a 1.a $1$ $56.642$ \(\Q\) None \(0\) \(3\) \(5\) \(20\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+20q^{7}+9q^{9}+56q^{11}+\cdots\)
960.4.a.bk 960.a 1.a $2$ $56.642$ \(\Q(\sqrt{89}) \) None \(0\) \(-6\) \(-10\) \(12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+(6+\beta )q^{7}+9q^{9}+(-12+\cdots)q^{11}+\cdots\)
960.4.a.bl 960.a 1.a $2$ $56.642$ \(\Q(\sqrt{201}) \) None \(0\) \(-6\) \(10\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+(2+\beta )q^{7}+9q^{9}-20q^{11}+\cdots\)
960.4.a.bm 960.a 1.a $2$ $56.642$ \(\Q(\sqrt{41}) \) None \(0\) \(-6\) \(10\) \(12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+(6+\beta )q^{7}+9q^{9}+(12+\cdots)q^{11}+\cdots\)
960.4.a.bn 960.a 1.a $2$ $56.642$ \(\Q(\sqrt{89}) \) None \(0\) \(6\) \(-10\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}+(-6-\beta )q^{7}+9q^{9}+\cdots\)
960.4.a.bo 960.a 1.a $2$ $56.642$ \(\Q(\sqrt{41}) \) None \(0\) \(6\) \(10\) \(-12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+(-6-\beta )q^{7}+9q^{9}+\cdots\)
960.4.a.bp 960.a 1.a $2$ $56.642$ \(\Q(\sqrt{201}) \) None \(0\) \(6\) \(10\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+5q^{5}+(-2-\beta )q^{7}+9q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(960))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(960)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 2}\)