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Properties

Label 200.6.q
Level $200$
Weight $6$
Character orbit 200.q
Rep. character $\chi_{200}(9,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $152$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 200.q (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(200, [\chi])\).

Total New Old
Modular forms 616 152 464
Cusp forms 584 152 432
Eisenstein series 32 0 32

Trace form

\( 152 q - 8 q^{5} + 3240 q^{9} + O(q^{10}) \) \( 152 q - 8 q^{5} + 3240 q^{9} + 726 q^{11} + 2212 q^{15} - 2166 q^{19} - 1764 q^{21} + 9570 q^{23} + 2136 q^{25} + 98 q^{29} + 9966 q^{31} - 19232 q^{35} - 50590 q^{37} + 2148 q^{39} - 25780 q^{41} - 52082 q^{45} - 33220 q^{47} - 375780 q^{49} - 92460 q^{51} - 87180 q^{53} + 17372 q^{55} - 12030 q^{59} - 100486 q^{61} - 106820 q^{63} - 3496 q^{65} + 109356 q^{69} - 75108 q^{71} + 83240 q^{73} - 222784 q^{75} - 119344 q^{79} - 23202 q^{81} + 260430 q^{83} - 66030 q^{85} - 229690 q^{87} + 93834 q^{89} + 243676 q^{91} - 159332 q^{95} + 247830 q^{97} + 507692 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)