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Properties

Label 1098.2.bj
Level $1098$
Weight $2$
Character orbit 1098.bj
Rep. character $\chi_{1098}(25,\cdot)$
Character field $\Q(\zeta_{15})$
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.bj (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 549 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 496 q - 124 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{9} + O(q^{10}) \) \( 496 q - 124 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{7} - 12 q^{9} - 2 q^{13} + 72 q^{14} - 12 q^{15} - 124 q^{16} - 12 q^{18} - 2 q^{19} + 4 q^{20} + 14 q^{21} - 8 q^{23} + 18 q^{24} + 62 q^{25} - 6 q^{27} - 6 q^{28} - 22 q^{29} + 2 q^{30} - 8 q^{31} - 34 q^{33} - 20 q^{35} - 2 q^{36} + 4 q^{37} - 22 q^{39} + 106 q^{41} - 8 q^{42} + 4 q^{43} + 34 q^{45} + 6 q^{46} - 2 q^{47} - 106 q^{49} + 12 q^{50} - 84 q^{51} - 2 q^{52} - 36 q^{53} - 8 q^{54} - 28 q^{56} - 2 q^{57} + 8 q^{60} - 62 q^{61} + 128 q^{62} - 8 q^{63} - 124 q^{64} - 40 q^{65} - 96 q^{66} - 14 q^{67} + 20 q^{69} + 18 q^{70} + 80 q^{71} + 8 q^{72} - 14 q^{73} + 192 q^{74} - 30 q^{75} + 18 q^{76} + 30 q^{77} + 40 q^{78} + 12 q^{79} + 4 q^{80} - 24 q^{81} - 12 q^{82} - 96 q^{83} - 26 q^{84} + 108 q^{85} - 8 q^{86} + 38 q^{87} + 76 q^{89} - 12 q^{90} + 26 q^{91} - 18 q^{92} + 178 q^{93} + 18 q^{94} + 20 q^{95} - 12 q^{96} - 24 q^{97} - 16 q^{98} - 102 q^{99} + O(q^{100}) \)

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

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