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Properties

Label 560.5.bx
Level $560$
Weight $5$
Character orbit 560.bx
Rep. character $\chi_{560}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 560.bx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(560, [\chi])\).

Total New Old
Modular forms 792 128 664
Cusp forms 744 128 616
Eisenstein series 48 0 48

Trace form

\( 128 q - 32 q^{7} + 1728 q^{9} + O(q^{10}) \) \( 128 q - 32 q^{7} + 1728 q^{9} - 96 q^{11} - 2496 q^{19} - 304 q^{21} + 576 q^{23} + 8000 q^{25} - 2784 q^{29} - 8832 q^{31} - 1824 q^{37} + 6144 q^{39} - 64 q^{43} + 1200 q^{45} - 1472 q^{49} - 3232 q^{51} - 2112 q^{53} + 7488 q^{57} + 9792 q^{59} + 12384 q^{61} + 23296 q^{63} + 1200 q^{65} - 17248 q^{67} - 5184 q^{71} + 11040 q^{73} - 18336 q^{77} - 12768 q^{79} - 45392 q^{81} - 68256 q^{87} - 10224 q^{89} - 38784 q^{91} + 13760 q^{93} - 80832 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)