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Properties

Label 1098.2.bo
Level $1098$
Weight $2$
Character orbit 1098.bo
Rep. character $\chi_{1098}(49,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $496$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 549 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(372\)

Dimensions

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

Total New Old
Modular forms 1520 496 1024
Cusp forms 1456 496 960
Eisenstein series 64 0 64

Trace form

\( 496 q - 62 q^{4} - 8 q^{5} - 6 q^{6} - 14 q^{7} - 18 q^{9} + O(q^{10}) \) \( 496 q - 62 q^{4} - 8 q^{5} - 6 q^{6} - 14 q^{7} - 18 q^{9} - 4 q^{13} - 36 q^{14} - 12 q^{15} + 62 q^{16} + 8 q^{18} + 2 q^{19} - 4 q^{20} - 6 q^{21} - 12 q^{23} + 4 q^{24} - 124 q^{25} - 30 q^{27} + 10 q^{28} + 26 q^{30} + 18 q^{33} - 2 q^{36} - 44 q^{39} + 100 q^{41} + 8 q^{42} - 6 q^{43} + 50 q^{45} + 6 q^{46} - 4 q^{47} - 32 q^{49} + 36 q^{50} - 48 q^{51} - 2 q^{52} + 140 q^{53} - 14 q^{56} - 60 q^{57} - 8 q^{60} - 50 q^{61} - 128 q^{62} + 92 q^{63} + 124 q^{64} - 4 q^{65} - 72 q^{66} - 32 q^{69} + 18 q^{70} + 16 q^{71} - 14 q^{73} + 64 q^{74} - 30 q^{75} - 6 q^{76} + 28 q^{77} + 50 q^{78} + 10 q^{79} + 4 q^{80} + 14 q^{81} + 36 q^{82} - 36 q^{83} + 14 q^{84} + 24 q^{85} - 88 q^{86} - 148 q^{87} + 6 q^{90} + 6 q^{91} - 80 q^{92} + 96 q^{93} - 30 q^{94} - 76 q^{95} + 10 q^{96} + 30 q^{97} + 18 q^{99} + O(q^{100}) \)

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

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