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Properties

Label 2156.2.bb
Level $2156$
Weight $2$
Character orbit 2156.bb
Rep. character $\chi_{2156}(111,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1680$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2156.bb (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2156, [\chi])\).

Total New Old
Modular forms 2040 1680 360
Cusp forms 1992 1680 312
Eisenstein series 48 0 48

Trace form

\( 1680 q + 12 q^{8} - 280 q^{9} + O(q^{10}) \) \( 1680 q + 12 q^{8} - 280 q^{9} + 70 q^{12} - 62 q^{14} + 8 q^{16} + 20 q^{18} + 16 q^{21} + 280 q^{25} - 32 q^{28} + 40 q^{29} - 32 q^{30} - 140 q^{34} + 20 q^{36} - 40 q^{37} + 112 q^{40} + 20 q^{44} + 20 q^{46} - 24 q^{49} + 228 q^{50} + 78 q^{56} + 48 q^{57} + 4 q^{58} + 40 q^{60} - 56 q^{61} - 12 q^{64} - 70 q^{66} + 148 q^{70} - 150 q^{72} - 210 q^{76} - 126 q^{78} - 480 q^{81} + 70 q^{82} + 28 q^{84} - 134 q^{86} - 266 q^{90} + 50 q^{92} - 16 q^{93} - 126 q^{94} - 490 q^{96} - 6 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2156, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)