Properties

Label 80.18.a
Level $80$
Weight $18$
Character orbit 80.a
Rep. character $\chi_{80}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $12$
Sturm bound $216$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(216\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(80))\).

Total New Old
Modular forms 210 34 176
Cusp forms 198 34 164
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
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(16\)
Minus space\(-\)\(18\)

Trace form

\( 34 q + 13122 q^{3} - 26311038 q^{7} + 1303838558 q^{9} - 8886916 q^{11} - 5125781250 q^{15} - 11440434244 q^{17} + 124198518528 q^{19} + 128106889532 q^{21} - 192886477450 q^{23} + 5187988281250 q^{25}+ \cdots + 22\!\cdots\!36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(80))\) 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
80.18.a.a 80.a 1.a $1$ $146.578$ \(\Q\) None 10.18.a.a \(0\) \(14976\) \(390625\) \(-14808668\) $-$ $-$ $\mathrm{SU}(2)$ \(q+14976q^{3}+5^{8}q^{5}-14808668q^{7}+\cdots\)
80.18.a.b 80.a 1.a $2$ $146.578$ \(\Q(\sqrt{2941}) \) None 10.18.a.d \(0\) \(-17628\) \(-781250\) \(-27684196\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-8814-\beta )q^{3}-5^{8}q^{5}+(-13842098+\cdots)q^{7}+\cdots\)
80.18.a.c 80.a 1.a $2$ $146.578$ \(\Q(\sqrt{247521}) \) None 20.18.a.a \(0\) \(-10980\) \(781250\) \(10044860\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-5490-\beta )q^{3}+5^{8}q^{5}+(5022430+\cdots)q^{7}+\cdots\)
80.18.a.d 80.a 1.a $2$ $146.578$ \(\Q(\sqrt{83281}) \) None 10.18.a.c \(0\) \(1308\) \(781250\) \(-603844\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(654-\beta )q^{3}+5^{8}q^{5}+(-301922+\cdots)q^{7}+\cdots\)
80.18.a.e 80.a 1.a $2$ $146.578$ \(\Q(\sqrt{36061}) \) None 10.18.a.b \(0\) \(6308\) \(-781250\) \(-6543844\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(3154-\beta )q^{3}-5^{8}q^{5}+(-3271922+\cdots)q^{7}+\cdots\)
80.18.a.f 80.a 1.a $2$ $146.578$ \(\Q(\sqrt{39}) \) None 5.18.a.a \(0\) \(10980\) \(-781250\) \(22820700\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(5490+13\beta )q^{3}-5^{8}q^{5}+(11410350+\cdots)q^{7}+\cdots\)
80.18.a.g 80.a 1.a $3$ $146.578$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 5.18.a.b \(0\) \(-15944\) \(1171875\) \(-2139308\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-5315-\beta _{2})q^{3}+5^{8}q^{5}+(-712892+\cdots)q^{7}+\cdots\)
80.18.a.h 80.a 1.a $3$ $146.578$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 20.18.a.b \(0\) \(2822\) \(-1171875\) \(7384698\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(941+\beta _{1})q^{3}-5^{8}q^{5}+(2461385+\cdots)q^{7}+\cdots\)
80.18.a.i 80.a 1.a $4$ $146.578$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 40.18.a.c \(0\) \(-4744\) \(1562500\) \(11958712\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1186+\beta _{1})q^{3}+5^{8}q^{5}+(2989678+\cdots)q^{7}+\cdots\)
80.18.a.j 80.a 1.a $4$ $146.578$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 40.18.a.b \(0\) \(936\) \(-1562500\) \(-15139688\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(234+\beta _{1})q^{3}-5^{8}q^{5}+(-3784922+\cdots)q^{7}+\cdots\)
80.18.a.k 80.a 1.a $4$ $146.578$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 40.18.a.a \(0\) \(9704\) \(-1562500\) \(-11287592\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(2426+\beta _{1})q^{3}-5^{8}q^{5}+(-2821898+\cdots)q^{7}+\cdots\)
80.18.a.l 80.a 1.a $5$ $146.578$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 40.18.a.d \(0\) \(15384\) \(1953125\) \(-312868\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(3077+\beta _{1})q^{3}+5^{8}q^{5}+(-62507+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(80))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(80)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)