Properties

Label 80.6.c
Level $80$
Weight $6$
Character orbit 80.c
Rep. character $\chi_{80}(49,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $4$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(80, [\chi])\).

Total New Old
Modular forms 66 16 50
Cusp forms 54 14 40
Eisenstein series 12 2 10

Trace form

\( 14q + 18q^{5} - 974q^{9} + O(q^{10}) \) \( 14q + 18q^{5} - 974q^{9} + 728q^{11} + 1192q^{15} - 984q^{19} + 1304q^{21} - 586q^{25} + 8260q^{29} - 9344q^{31} - 12712q^{35} + 10544q^{39} + 3580q^{41} - 10578q^{45} - 31222q^{49} + 73088q^{51} + 22952q^{55} - 69896q^{59} + 21748q^{61} + 4016q^{65} - 21096q^{69} - 47792q^{71} - 85584q^{75} + 82912q^{79} + 141254q^{81} - 97920q^{85} + 110188q^{89} + 105680q^{91} - 195752q^{95} - 152024q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
80.6.c.a \(2\) \(12.831\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-90\) \(0\) \(q-3\beta q^{3}+(-45-5\beta )q^{5}-9\beta q^{7}+\cdots\)
80.6.c.b \(2\) \(12.831\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(-10\) \(0\) \(q-\beta q^{3}+(-5+5\beta )q^{5}-11\beta q^{7}+119q^{9}+\cdots\)
80.6.c.c \(2\) \(12.831\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) \(q+7iq^{3}+(55-5i)q^{5}-79iq^{7}+47q^{9}+\cdots\)
80.6.c.d \(8\) \(12.831\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)