Properties

Label 80.6.a
Level $80$
Weight $6$
Character orbit 80.a
Rep. character $\chi_{80}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $9$
Sturm bound $72$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(80))\).

Total New Old
Modular forms 66 10 56
Cusp forms 54 10 44
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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(6\)

Trace form

\( 10q + 18q^{3} - 222q^{7} + 854q^{9} + O(q^{10}) \) \( 10q + 18q^{3} - 222q^{7} + 854q^{9} + 604q^{11} - 450q^{15} + 1004q^{17} + 4416q^{19} - 820q^{21} - 4010q^{23} + 6250q^{25} + 9564q^{27} + 8052q^{29} - 756q^{31} - 1920q^{33} + 7350q^{35} - 10648q^{37} + 42948q^{39} - 10624q^{41} - 41918q^{43} + 5900q^{45} - 19582q^{47} + 45022q^{49} - 50540q^{51} - 42240q^{53} - 12100q^{55} - 60888q^{57} - 37000q^{59} + 36608q^{61} + 754q^{63} + 21100q^{65} + 70630q^{67} - 84764q^{69} - 64308q^{71} - 106196q^{73} + 11250q^{75} + 67376q^{77} - 22792q^{79} + 88118q^{81} + 229210q^{83} - 66200q^{85} - 34932q^{87} - 138108q^{89} + 24788q^{91} + 329192q^{93} - 72200q^{95} + 40772q^{97} - 32596q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(80))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
80.6.a.a \(1\) \(12.831\) \(\Q\) None \(0\) \(-24\) \(25\) \(172\) \(-\) \(-\) \(q-24q^{3}+5^{2}q^{5}+172q^{7}+333q^{9}+\cdots\)
80.6.a.b \(1\) \(12.831\) \(\Q\) None \(0\) \(-22\) \(-25\) \(-218\) \(-\) \(+\) \(q-22q^{3}-5^{2}q^{5}-218q^{7}+241q^{9}+\cdots\)
80.6.a.c \(1\) \(12.831\) \(\Q\) None \(0\) \(-6\) \(-25\) \(118\) \(-\) \(+\) \(q-6q^{3}-5^{2}q^{5}+118q^{7}-207q^{9}+\cdots\)
80.6.a.d \(1\) \(12.831\) \(\Q\) None \(0\) \(2\) \(-25\) \(62\) \(+\) \(+\) \(q+2q^{3}-5^{2}q^{5}+62q^{7}-239q^{9}+\cdots\)
80.6.a.e \(1\) \(12.831\) \(\Q\) None \(0\) \(4\) \(25\) \(-192\) \(-\) \(-\) \(q+4q^{3}+5^{2}q^{5}-192q^{7}-227q^{9}+\cdots\)
80.6.a.f \(1\) \(12.831\) \(\Q\) None \(0\) \(8\) \(25\) \(108\) \(+\) \(-\) \(q+8q^{3}+5^{2}q^{5}+108q^{7}-179q^{9}+\cdots\)
80.6.a.g \(1\) \(12.831\) \(\Q\) None \(0\) \(18\) \(-25\) \(-242\) \(+\) \(+\) \(q+18q^{3}-5^{2}q^{5}-242q^{7}+3^{4}q^{9}+\cdots\)
80.6.a.h \(1\) \(12.831\) \(\Q\) None \(0\) \(26\) \(-25\) \(22\) \(-\) \(+\) \(q+26q^{3}-5^{2}q^{5}+22q^{7}+433q^{9}+\cdots\)
80.6.a.i \(2\) \(12.831\) \(\Q(\sqrt{129}) \) None \(0\) \(12\) \(50\) \(-52\) \(+\) \(-\) \(q+(6+\beta )q^{3}+5^{2}q^{5}+(-26+3\beta )q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(80))\) into lower level spaces

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