Properties

Label 320.6.a
Level $320$
Weight $6$
Character orbit 320.a
Rep. character $\chi_{320}(1,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $26$
Sturm bound $288$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(288\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(320))\).

Total New Old
Modular forms 252 40 212
Cusp forms 228 40 188
Eisenstein series 24 0 24

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

\(2\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(18\)
Minus space\(-\)\(22\)

Trace form

\( 40 q + 3240 q^{9} + O(q^{10}) \) \( 40 q + 3240 q^{9} + 464 q^{13} - 8496 q^{21} + 25000 q^{25} - 8144 q^{29} - 11344 q^{33} + 25600 q^{37} + 23216 q^{41} + 96040 q^{49} + 49456 q^{53} + 61616 q^{57} + 52224 q^{61} + 22320 q^{69} + 14896 q^{77} + 215176 q^{81} + 132400 q^{85} + 6320 q^{89} + 9312 q^{93} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(320))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
320.6.a.a $1$ $51.323$ \(\Q\) None \(0\) \(-26\) \(25\) \(22\) $-$ $-$ \(q-26q^{3}+5^{2}q^{5}+22q^{7}+433q^{9}+\cdots\)
320.6.a.b $1$ $51.323$ \(\Q\) None \(0\) \(-24\) \(-25\) \(-172\) $+$ $+$ \(q-24q^{3}-5^{2}q^{5}-172q^{7}+333q^{9}+\cdots\)
320.6.a.c $1$ $51.323$ \(\Q\) None \(0\) \(-22\) \(25\) \(218\) $+$ $-$ \(q-22q^{3}+5^{2}q^{5}+218q^{7}+241q^{9}+\cdots\)
320.6.a.d $1$ $51.323$ \(\Q\) None \(0\) \(-18\) \(25\) \(-242\) $-$ $-$ \(q-18q^{3}+5^{2}q^{5}-242q^{7}+3^{4}q^{9}+\cdots\)
320.6.a.e $1$ $51.323$ \(\Q\) None \(0\) \(-8\) \(-25\) \(108\) $-$ $+$ \(q-8q^{3}-5^{2}q^{5}+108q^{7}-179q^{9}+\cdots\)
320.6.a.f $1$ $51.323$ \(\Q\) None \(0\) \(-6\) \(25\) \(-118\) $+$ $-$ \(q-6q^{3}+5^{2}q^{5}-118q^{7}-207q^{9}+\cdots\)
320.6.a.g $1$ $51.323$ \(\Q\) None \(0\) \(-4\) \(-25\) \(-192\) $-$ $+$ \(q-4q^{3}-5^{2}q^{5}-192q^{7}-227q^{9}+\cdots\)
320.6.a.h $1$ $51.323$ \(\Q\) None \(0\) \(-2\) \(25\) \(62\) $-$ $-$ \(q-2q^{3}+5^{2}q^{5}+62q^{7}-239q^{9}+\cdots\)
320.6.a.i $1$ $51.323$ \(\Q\) None \(0\) \(2\) \(25\) \(-62\) $+$ $-$ \(q+2q^{3}+5^{2}q^{5}-62q^{7}-239q^{9}+\cdots\)
320.6.a.j $1$ $51.323$ \(\Q\) None \(0\) \(4\) \(-25\) \(192\) $+$ $+$ \(q+4q^{3}-5^{2}q^{5}+192q^{7}-227q^{9}+\cdots\)
320.6.a.k $1$ $51.323$ \(\Q\) None \(0\) \(6\) \(25\) \(118\) $-$ $-$ \(q+6q^{3}+5^{2}q^{5}+118q^{7}-207q^{9}+\cdots\)
320.6.a.l $1$ $51.323$ \(\Q\) None \(0\) \(8\) \(-25\) \(-108\) $+$ $+$ \(q+8q^{3}-5^{2}q^{5}-108q^{7}-179q^{9}+\cdots\)
320.6.a.m $1$ $51.323$ \(\Q\) None \(0\) \(18\) \(25\) \(242\) $+$ $-$ \(q+18q^{3}+5^{2}q^{5}+242q^{7}+3^{4}q^{9}+\cdots\)
320.6.a.n $1$ $51.323$ \(\Q\) None \(0\) \(22\) \(25\) \(-218\) $-$ $-$ \(q+22q^{3}+5^{2}q^{5}-218q^{7}+241q^{9}+\cdots\)
320.6.a.o $1$ $51.323$ \(\Q\) None \(0\) \(24\) \(-25\) \(172\) $-$ $+$ \(q+24q^{3}-5^{2}q^{5}+172q^{7}+333q^{9}+\cdots\)
320.6.a.p $1$ $51.323$ \(\Q\) None \(0\) \(26\) \(25\) \(-22\) $+$ $-$ \(q+26q^{3}+5^{2}q^{5}-22q^{7}+433q^{9}+\cdots\)
320.6.a.q $2$ $51.323$ \(\Q(\sqrt{129}) \) None \(0\) \(-12\) \(-50\) \(-52\) $-$ $+$ \(q+(-6-\beta )q^{3}-5^{2}q^{5}+(-26+3\beta )q^{7}+\cdots\)
320.6.a.r $2$ $51.323$ \(\Q(\sqrt{70}) \) None \(0\) \(-8\) \(-50\) \(104\) $+$ $+$ \(q+(-4+\beta )q^{3}-5^{2}q^{5}+(52+\beta )q^{7}+\cdots\)
320.6.a.s $2$ $51.323$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-50\) \(0\) $-$ $+$ \(q+\beta q^{3}-5^{2}q^{5}-7\beta q^{7}-203q^{9}+\cdots\)
320.6.a.t $2$ $51.323$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(50\) \(0\) $-$ $-$ \(q-3\beta q^{3}+5^{2}q^{5}+31\beta q^{7}-63q^{9}+\cdots\)
320.6.a.u $2$ $51.323$ \(\Q(\sqrt{85}) \) None \(0\) \(0\) \(50\) \(0\) $-$ $-$ \(q-\beta q^{3}+5^{2}q^{5}-3\beta q^{7}+97q^{9}+26\beta q^{11}+\cdots\)
320.6.a.v $2$ $51.323$ \(\Q(\sqrt{70}) \) None \(0\) \(8\) \(-50\) \(-104\) $+$ $+$ \(q+(4+\beta )q^{3}-5^{2}q^{5}+(-52+\beta )q^{7}+\cdots\)
320.6.a.w $2$ $51.323$ \(\Q(\sqrt{129}) \) None \(0\) \(12\) \(-50\) \(52\) $+$ $+$ \(q+(6+\beta )q^{3}-5^{2}q^{5}+(26-3\beta )q^{7}+\cdots\)
320.6.a.x $3$ $51.323$ 3.3.39180.1 None \(0\) \(-10\) \(75\) \(-6\) $+$ $-$ \(q+(-3-\beta _{1})q^{3}+5^{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
320.6.a.y $3$ $51.323$ 3.3.39180.1 None \(0\) \(10\) \(75\) \(6\) $+$ $-$ \(q+(3+\beta _{1})q^{3}+5^{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
320.6.a.z $4$ $51.323$ 4.4.81998080.1 None \(0\) \(0\) \(-100\) \(0\) $-$ $+$ \(q-\beta _{1}q^{3}-5^{2}q^{5}+(6\beta _{1}-\beta _{2})q^{7}+(181+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(320))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(320)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)