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Properties

Label 1098.2.bh
Level $1098$
Weight $2$
Character orbit 1098.bh
Rep. character $\chi_{1098}(101,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $248$
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.bh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 549 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(372\)

Dimensions

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

Total New Old
Modular forms 760 248 512
Cusp forms 728 248 480
Eisenstein series 32 0 32

Trace form

\( 248 q - 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 248 q - 8 q^{6} - 4 q^{7} - 16 q^{15} + 124 q^{16} + 16 q^{18} - 20 q^{21} + 12 q^{23} + 8 q^{24} + 248 q^{25} - 4 q^{28} + 48 q^{29} + 4 q^{31} - 16 q^{33} + 60 q^{35} + 12 q^{36} + 4 q^{37} + 36 q^{39} - 12 q^{41} - 8 q^{43} - 36 q^{46} - 12 q^{49} + 28 q^{51} + 12 q^{52} - 48 q^{53} - 4 q^{54} + 32 q^{57} + 28 q^{61} - 32 q^{63} - 48 q^{66} + 28 q^{67} - 20 q^{69} - 24 q^{70} + 48 q^{71} - 8 q^{72} + 28 q^{73} + 96 q^{74} + 8 q^{76} - 76 q^{78} + 4 q^{79} - 20 q^{81} + 24 q^{82} - 36 q^{83} - 16 q^{84} - 48 q^{85} + 48 q^{86} + 76 q^{87} + 12 q^{89} - 104 q^{90} + 24 q^{91} - 24 q^{92} + 32 q^{93} - 12 q^{94} + 120 q^{95} - 4 q^{96} - 48 q^{98} + 112 q^{99} + O(q^{100}) \)

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

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