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Properties

Label 1098.2.n
Level $1098$
Weight $2$
Character orbit 1098.n
Rep. character $\chi_{1098}(841,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $124$
Sturm bound $372$

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Defining parameters

Level: \( N \) \(=\) \( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1098.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 549 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(372\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1098, [\chi])\).

Total New Old
Modular forms 380 124 256
Cusp forms 364 124 240
Eisenstein series 16 0 16

Trace form

\( 124 q - 124 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{9} + O(q^{10}) \) \( 124 q - 124 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{9} - 2 q^{13} + 8 q^{14} - 8 q^{15} + 124 q^{16} - 2 q^{19} + 4 q^{20} + 6 q^{21} - 12 q^{23} - 6 q^{24} - 62 q^{25} - 12 q^{29} - 12 q^{33} + 2 q^{36} - 36 q^{39} - 30 q^{41} - 8 q^{42} + 44 q^{45} - 6 q^{46} - 2 q^{47} - 104 q^{49} + 36 q^{50} + 42 q^{51} + 2 q^{52} - 8 q^{56} + 46 q^{57} + 8 q^{60} - 20 q^{61} - 32 q^{62} + 54 q^{63} - 124 q^{64} + 8 q^{65} + 8 q^{66} - 42 q^{67} - 12 q^{69} + 12 q^{70} + 24 q^{71} + 14 q^{73} - 72 q^{74} - 30 q^{75} + 2 q^{76} + 14 q^{77} - 4 q^{80} + 26 q^{81} - 36 q^{82} + 28 q^{83} - 6 q^{84} - 36 q^{85} - 16 q^{86} + 24 q^{90} - 6 q^{91} + 12 q^{92} - 30 q^{93} - 4 q^{95} + 6 q^{96} + 10 q^{97} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1098, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1098, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1098, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(549, [\chi])\)\(^{\oplus 2}\)