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Properties

Label 230.6.l
Level $230$
Weight $6$
Character orbit 230.l
Rep. character $\chi_{230}(7,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1200$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.l (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(216\)

Dimensions

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

Total New Old
Modular forms 3680 1200 2480
Cusp forms 3520 1200 2320
Eisenstein series 160 0 160

Trace form

\( 1200 q - 8 q^{3} + 160 q^{6} + O(q^{10}) \) \( 1200 q - 8 q^{3} + 160 q^{6} - 128 q^{12} + 2096 q^{13} + 30720 q^{16} + 20448 q^{18} - 46880 q^{23} + 9440 q^{25} + 1760 q^{26} + 4816 q^{27} + 41536 q^{28} + 11320 q^{31} - 165044 q^{33} - 25288 q^{35} - 143360 q^{36} + 144232 q^{37} - 8520 q^{41} - 51840 q^{46} - 98480 q^{47} + 2048 q^{48} + 2848 q^{50} + 33536 q^{52} - 52480 q^{55} + 14080 q^{56} + 56232 q^{57} + 500720 q^{61} - 43072 q^{62} - 630080 q^{66} + 124704 q^{70} - 1220880 q^{71} - 72704 q^{72} + 64312 q^{73} - 698756 q^{75} - 461704 q^{77} - 100320 q^{78} + 1582520 q^{81} - 221280 q^{82} - 430580 q^{85} - 1266320 q^{86} + 754760 q^{87} - 100992 q^{92} - 670504 q^{93} + 1012292 q^{95} - 40960 q^{96} + 1165692 q^{97} - 24096 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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