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Properties

Label 280.6.bo
Level $280$
Weight $6$
Character orbit 280.bo
Rep. character $\chi_{280}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.bo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(280, [\chi])\).

Total New Old
Modular forms 992 240 752
Cusp forms 928 240 688
Eisenstein series 64 0 64

Trace form

\( 240 q + 76 q^{7} + O(q^{10}) \) \( 240 q + 76 q^{7} + 20 q^{11} - 792 q^{15} + 1580 q^{21} - 1444 q^{23} + 2552 q^{25} + 42444 q^{33} - 30216 q^{35} - 13112 q^{37} + 23984 q^{43} + 5808 q^{45} - 74280 q^{51} + 8336 q^{53} + 1504 q^{57} + 140220 q^{61} + 6012 q^{63} - 52308 q^{65} - 59216 q^{67} + 167680 q^{71} - 99888 q^{73} + 56592 q^{75} + 68884 q^{77} + 812400 q^{81} - 103880 q^{85} - 335772 q^{87} + 534000 q^{91} + 108960 q^{93} + 113304 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)