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Properties

Label 2898.2.bx
Level $2898$
Weight $2$
Character orbit 2898.bx
Rep. character $\chi_{2898}(163,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $1600$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2898.bx (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2898, [\chi])\).

Total New Old
Modular forms 11840 1600 10240
Cusp forms 11200 1600 9600
Eisenstein series 640 0 640

Trace form

\( 1600 q + 80 q^{4} - 8 q^{5} + 4 q^{7} + O(q^{10}) \) \( 1600 q + 80 q^{4} - 8 q^{5} + 4 q^{7} + 4 q^{10} - 8 q^{11} + 12 q^{14} + 80 q^{16} - 28 q^{20} + 16 q^{22} - 40 q^{23} + 32 q^{25} + 4 q^{26} + 36 q^{28} - 16 q^{29} - 4 q^{31} - 32 q^{34} - 10 q^{35} + 44 q^{37} - 20 q^{38} + 4 q^{40} - 40 q^{41} - 64 q^{43} - 8 q^{44} - 16 q^{46} + 8 q^{47} - 6 q^{49} + 32 q^{50} - 40 q^{55} + 10 q^{56} - 44 q^{58} - 28 q^{59} + 140 q^{61} + 24 q^{62} - 160 q^{64} - 142 q^{65} + 8 q^{67} + 88 q^{68} + 60 q^{70} + 64 q^{71} - 8 q^{73} + 8 q^{74} + 110 q^{77} - 64 q^{79} - 8 q^{80} + 88 q^{82} - 104 q^{83} - 52 q^{85} - 30 q^{86} - 8 q^{88} - 28 q^{89} + 28 q^{91} - 8 q^{92} + 28 q^{94} - 18 q^{95} + 88 q^{97} + 12 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2898, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2898, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2898, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(966, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1449, [\chi])\)\(^{\oplus 2}\)