Properties

Label 80.12.a
Level $80$
Weight $12$
Character orbit 80.a
Rep. character $\chi_{80}(1,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $13$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(80))\).

Total New Old
Modular forms 138 22 116
Cusp forms 126 22 104
Eisenstein series 12 0 12

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
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(10\)

Trace form

\( 22 q - 486 q^{3} + 136306 q^{7} + 1091834 q^{9} + 540844 q^{11} + 1518750 q^{15} - 7412332 q^{17} - 18693312 q^{19} - 12566044 q^{21} + 31878310 q^{23} + 214843750 q^{25} - 181608852 q^{27} + 174163452 q^{29}+ \cdots + 251845394780 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(80))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
80.12.a.a 80.a 1.a $1$ $61.467$ \(\Q\) None 10.12.a.b \(0\) \(-738\) \(-3125\) \(-25574\) $-$ $+$ $\mathrm{SU}(2)$ \(q-738q^{3}-5^{5}q^{5}-25574q^{7}+367497q^{9}+\cdots\)
80.12.a.b 80.a 1.a $1$ $61.467$ \(\Q\) None 40.12.a.a \(0\) \(-520\) \(3125\) \(-15148\) $+$ $-$ $\mathrm{SU}(2)$ \(q-520q^{3}+5^{5}q^{5}-15148q^{7}+93253q^{9}+\cdots\)
80.12.a.c 80.a 1.a $1$ $61.467$ \(\Q\) None 20.12.a.a \(0\) \(-306\) \(-3125\) \(32074\) $-$ $+$ $\mathrm{SU}(2)$ \(q-306q^{3}-5^{5}q^{5}+32074q^{7}-83511q^{9}+\cdots\)
80.12.a.d 80.a 1.a $1$ $61.467$ \(\Q\) None 10.12.a.a \(0\) \(12\) \(3125\) \(14176\) $-$ $-$ $\mathrm{SU}(2)$ \(q+12q^{3}+5^{5}q^{5}+14176q^{7}-177003q^{9}+\cdots\)
80.12.a.e 80.a 1.a $1$ $61.467$ \(\Q\) None 10.12.a.c \(0\) \(318\) \(-3125\) \(70714\) $-$ $+$ $\mathrm{SU}(2)$ \(q+318q^{3}-5^{5}q^{5}+70714q^{7}-76023q^{9}+\cdots\)
80.12.a.f 80.a 1.a $1$ $61.467$ \(\Q\) None 5.12.a.a \(0\) \(792\) \(3125\) \(17556\) $-$ $-$ $\mathrm{SU}(2)$ \(q+792q^{3}+5^{5}q^{5}+17556q^{7}+450117q^{9}+\cdots\)
80.12.a.g 80.a 1.a $2$ $61.467$ \(\Q(\sqrt{1969}) \) None 10.12.a.d \(0\) \(-604\) \(6250\) \(-14092\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-302-\beta )q^{3}+5^{5}q^{5}+(-7046+\cdots)q^{7}+\cdots\)
80.12.a.h 80.a 1.a $2$ $61.467$ \(\Q(\sqrt{57}) \) None 40.12.a.c \(0\) \(-252\) \(6250\) \(24212\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-126-\beta )q^{3}+5^{5}q^{5}+(12106+\cdots)q^{7}+\cdots\)
80.12.a.i 80.a 1.a $2$ $61.467$ \(\Q(\sqrt{46729}) \) None 20.12.a.b \(0\) \(-220\) \(6250\) \(-3340\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-110-\beta )q^{3}+5^{5}q^{5}+(-1670+\cdots)q^{7}+\cdots\)
80.12.a.j 80.a 1.a $2$ $61.467$ \(\Q(\sqrt{151}) \) None 5.12.a.b \(0\) \(220\) \(-6250\) \(-57900\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(110+\beta )q^{3}-5^{5}q^{5}+(-28950+\cdots)q^{7}+\cdots\)
80.12.a.k 80.a 1.a $2$ $61.467$ \(\Q(\sqrt{42421}) \) None 40.12.a.b \(0\) \(792\) \(6250\) \(-5632\) $+$ $-$ $\mathrm{SU}(2)$ \(q+396q^{3}+5^{5}q^{5}+(-2816+\beta )q^{7}+\cdots\)
80.12.a.l 80.a 1.a $3$ $61.467$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 40.12.a.e \(0\) \(-78\) \(-9375\) \(-1530\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-26-\beta _{1})q^{3}-5^{5}q^{5}+(-510+\cdots)q^{7}+\cdots\)
80.12.a.m 80.a 1.a $3$ $61.467$ 3.3.229897.1 None 40.12.a.d \(0\) \(98\) \(-9375\) \(100790\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(33+\beta _{1})q^{3}-5^{5}q^{5}+(33580-3^{3}\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(80))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(80)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)