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Properties

Label 80.20.n
Level $80$
Weight $20$
Character orbit 80.n
Rep. character $\chi_{80}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $114$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(80, [\chi])\).

Total New Old
Modular forms 468 114 354
Cusp forms 444 114 330
Eisenstein series 24 0 24

Trace form

\( 114 q + O(q^{10}) \) \( 114 q + 112923669462 q^{13} - 42364280082 q^{17} - 9918902588136 q^{21} + 26973862521054 q^{25} + 689032218787272 q^{33} + 3952603949871810 q^{37} + 7850498798737416 q^{41} + 20722645429408530 q^{45} - 79098121985181294 q^{53} - 250767500076504336 q^{57} + 506915487237623778 q^{65} + 1700055099800182266 q^{73} + 1296318837845656488 q^{77} - 15232653158202723018 q^{81} - 14225328500192394426 q^{85} + 42790646876642334168 q^{93} + 4693473982793794794 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(80, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{20}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

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