Properties

Label 80.4.c
Level $80$
Weight $4$
Character orbit 80.c
Rep. character $\chi_{80}(49,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 80.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(80, [\chi])\).

Total New Old
Modular forms 42 10 32
Cusp forms 30 8 22
Eisenstein series 12 2 10

Trace form

\( 8 q - 56 q^{9} + O(q^{10}) \) \( 8 q - 56 q^{9} - 64 q^{11} - 32 q^{15} + 128 q^{19} - 16 q^{21} + 72 q^{25} + 112 q^{29} + 320 q^{31} - 64 q^{35} - 640 q^{39} - 32 q^{41} - 144 q^{45} + 360 q^{49} - 448 q^{51} + 1056 q^{55} + 1408 q^{59} + 64 q^{61} - 544 q^{65} - 720 q^{69} + 64 q^{71} - 2688 q^{75} - 3008 q^{79} + 56 q^{81} + 1088 q^{85} - 752 q^{89} - 704 q^{91} + 3232 q^{95} + 6400 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.4.c.a $2$ $4.720$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+iq^{3}+(-5-5i)q^{5}-13iq^{7}+23q^{9}+\cdots\)
80.4.c.b $2$ $4.720$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(14\) \(0\) \(q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
80.4.c.c $4$ $4.720$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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