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Properties

Label 620.3.bi
Level $620$
Weight $3$
Character orbit 620.bi
Rep. character $\chi_{620}(33,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $256$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 620.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(620, [\chi])\).

Total New Old
Modular forms 1584 256 1328
Cusp forms 1488 256 1232
Eisenstein series 96 0 96

Trace form

\( 256 q - 4 q^{3} - 24 q^{7} + O(q^{10}) \) \( 256 q - 4 q^{3} - 24 q^{7} - 16 q^{15} + 72 q^{21} - 62 q^{23} + 76 q^{25} - 190 q^{27} + 28 q^{31} + 148 q^{33} - 132 q^{35} + 244 q^{37} - 108 q^{41} + 168 q^{43} - 88 q^{45} - 216 q^{47} + 56 q^{51} + 180 q^{53} + 280 q^{55} + 52 q^{57} - 208 q^{61} + 304 q^{63} + 274 q^{65} + 204 q^{67} + 36 q^{71} - 88 q^{73} - 962 q^{75} + 612 q^{77} + 1008 q^{81} - 974 q^{83} + 624 q^{85} + 268 q^{87} - 152 q^{91} - 132 q^{93} + 64 q^{95} - 278 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(620, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(620, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(620, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)