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Properties

Label 1098.2.cg
Level $1098$
Weight $2$
Character orbit 1098.cg
Rep. character $\chi_{1098}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $992$
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.cg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 549 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(372\)

Dimensions

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

Total New Old
Modular forms 3040 992 2048
Cusp forms 2912 992 1920
Eisenstein series 128 0 128

Trace form

\( 992 q + 8 q^{6} + 4 q^{7} + O(q^{10}) \) \( 992 q + 8 q^{6} + 4 q^{7} + 48 q^{15} - 124 q^{16} + 8 q^{18} - 4 q^{21} - 60 q^{23} + 4 q^{24} + 124 q^{25} + 120 q^{27} - 8 q^{28} - 156 q^{29} - 8 q^{30} - 4 q^{31} - 8 q^{33} + 8 q^{37} - 200 q^{39} + 60 q^{41} - 4 q^{43} + 100 q^{45} + 20 q^{49} - 72 q^{50} - 28 q^{51} + 4 q^{54} + 160 q^{57} + 112 q^{61} - 16 q^{63} + 240 q^{66} - 28 q^{67} - 16 q^{69} - 36 q^{70} - 16 q^{72} - 112 q^{73} + 96 q^{74} + 12 q^{76} + 96 q^{77} - 44 q^{78} - 4 q^{79} - 20 q^{81} + 48 q^{82} + 72 q^{83} - 24 q^{84} - 24 q^{85} + 144 q^{86} + 68 q^{87} - 4 q^{90} + 48 q^{91} - 120 q^{92} - 100 q^{93} + 12 q^{94} - 120 q^{95} + 4 q^{96} + 68 q^{99} + O(q^{100}) \)

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

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