Properties

Label 230.6.e
Level $230$
Weight $6$
Character orbit 230.e
Rep. character $\chi_{230}(137,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(230, [\chi])\).

Total New Old
Modular forms 368 120 248
Cusp forms 352 120 232
Eisenstein series 16 0 16

Trace form

\( 120q + 8q^{3} - 160q^{6} + O(q^{10}) \) \( 120q + 8q^{3} - 160q^{6} + 128q^{12} - 2096q^{13} - 30720q^{16} + 4544q^{18} + 6312q^{23} - 9440q^{25} - 1760q^{26} - 4816q^{27} - 11320q^{31} + 25288q^{35} + 143360q^{36} + 8520q^{41} + 51840q^{46} - 47688q^{47} - 2048q^{48} - 2848q^{50} - 33536q^{52} + 52480q^{55} + 43072q^{62} - 124704q^{70} - 189320q^{71} + 72704q^{72} - 64312q^{73} + 102072q^{75} + 461704q^{77} + 100320q^{78} - 536200q^{81} + 221280q^{82} + 459576q^{85} - 754760q^{87} + 100992q^{92} + 670504q^{93} + 176544q^{95} + 40960q^{96} + 13184q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)