Properties

Label 80.10.a
Level $80$
Weight $10$
Character orbit 80.a
Rep. character $\chi_{80}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $11$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(80))\).

Total New Old
Modular forms 114 18 96
Cusp forms 102 18 84
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
\(+\)\(+\)$+$\(4\)
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(8\)
Minus space\(-\)\(10\)

Trace form

\( 18 q + 162 q^{3} - 2750 q^{7} + 145838 q^{9} + O(q^{10}) \) \( 18 q + 162 q^{3} - 2750 q^{7} + 145838 q^{9} - 65860 q^{11} - 101250 q^{15} - 242212 q^{17} - 429696 q^{19} + 317084 q^{21} + 53942 q^{23} + 7031250 q^{25} + 10576572 q^{27} - 2572316 q^{29} - 18789876 q^{31} + 9585408 q^{33} + 9003750 q^{35} - 1214776 q^{37} - 45636732 q^{39} - 5888256 q^{41} + 103684082 q^{43} - 6902500 q^{45} - 103174654 q^{47} + 133620662 q^{49} + 220753972 q^{51} + 54219264 q^{53} - 36602500 q^{55} + 10596936 q^{57} + 158263288 q^{59} + 155249152 q^{61} - 118675982 q^{63} - 87902500 q^{65} + 730750038 q^{67} - 206565164 q^{69} + 87544716 q^{71} + 52841052 q^{73} + 63281250 q^{75} + 160708208 q^{77} + 1224570360 q^{79} + 1368858734 q^{81} - 754085846 q^{83} + 214605000 q^{85} - 136660980 q^{87} - 997034220 q^{89} - 2165382476 q^{91} + 803195336 q^{93} - 651605000 q^{95} + 1276631188 q^{97} - 5943909556 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(80))\) 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 5
80.10.a.a 80.a 1.a $1$ $41.203$ \(\Q\) None \(0\) \(-174\) \(-625\) \(-4658\) $-$ $+$ $\mathrm{SU}(2)$ \(q-174q^{3}-5^{4}q^{5}-4658q^{7}+10593q^{9}+\cdots\)
80.10.a.b 80.a 1.a $1$ $41.203$ \(\Q\) None \(0\) \(-46\) \(-625\) \(10318\) $-$ $+$ $\mathrm{SU}(2)$ \(q-46q^{3}-5^{4}q^{5}+10318q^{7}-17567q^{9}+\cdots\)
80.10.a.c 80.a 1.a $1$ $41.203$ \(\Q\) None \(0\) \(48\) \(625\) \(532\) $-$ $-$ $\mathrm{SU}(2)$ \(q+48q^{3}+5^{4}q^{5}+532q^{7}-17379q^{9}+\cdots\)
80.10.a.d 80.a 1.a $1$ $41.203$ \(\Q\) None \(0\) \(114\) \(-625\) \(-4242\) $-$ $+$ $\mathrm{SU}(2)$ \(q+114q^{3}-5^{4}q^{5}-4242q^{7}-6687q^{9}+\cdots\)
80.10.a.e 80.a 1.a $1$ $41.203$ \(\Q\) None \(0\) \(204\) \(625\) \(-5432\) $-$ $-$ $\mathrm{SU}(2)$ \(q+204q^{3}+5^{4}q^{5}-5432q^{7}+21933q^{9}+\cdots\)
80.10.a.f 80.a 1.a $2$ $41.203$ \(\Q(\sqrt{1009}) \) None \(0\) \(-260\) \(1250\) \(-1700\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-130-\beta )q^{3}+5^{4}q^{5}+(-850+\cdots)q^{7}+\cdots\)
80.10.a.g 80.a 1.a $2$ $41.203$ \(\Q(\sqrt{46}) \) None \(0\) \(-108\) \(-1250\) \(908\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-54+\beta )q^{3}-5^{4}q^{5}+(454+13\beta )q^{7}+\cdots\)
80.10.a.h 80.a 1.a $2$ $41.203$ \(\Q(\sqrt{6049}) \) None \(0\) \(92\) \(1250\) \(6908\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(46-\beta )q^{3}+5^{4}q^{5}+(3454+37\beta )q^{7}+\cdots\)
80.10.a.i 80.a 1.a $2$ $41.203$ \(\Q(\sqrt{22}) \) None \(0\) \(116\) \(-1250\) \(-11284\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(58+\beta )q^{3}-5^{4}q^{5}+(-5642-35\beta )q^{7}+\cdots\)
80.10.a.j 80.a 1.a $2$ $41.203$ \(\Q(\sqrt{79}) \) None \(0\) \(260\) \(-1250\) \(380\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(130+\beta )q^{3}-5^{4}q^{5}+(190+69\beta )q^{7}+\cdots\)
80.10.a.k 80.a 1.a $3$ $41.203$ 3.3.7117.1 None \(0\) \(-84\) \(1875\) \(5520\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-28-\beta _{1})q^{3}+5^{4}q^{5}+(1840-17\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(80))\) into lower level spaces

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