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Properties

Label 2156.2.l
Level $2156$
Weight $2$
Character orbit 2156.l
Rep. character $\chi_{2156}(815,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $400$
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.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 704 400 304
Cusp forms 640 400 240
Eisenstein series 64 0 64

Trace form

\( 400 q - 12 q^{8} - 200 q^{9} + O(q^{10}) \) \( 400 q - 12 q^{8} - 200 q^{9} + 18 q^{10} + 30 q^{12} + 4 q^{16} + 10 q^{18} + 200 q^{25} - 30 q^{26} + 16 q^{29} - 56 q^{30} + 40 q^{32} + 60 q^{36} + 8 q^{37} + 12 q^{38} + 60 q^{40} - 4 q^{44} - 24 q^{45} + 10 q^{46} + 104 q^{50} - 54 q^{52} + 30 q^{54} - 112 q^{57} - 22 q^{58} + 4 q^{60} + 60 q^{64} + 32 q^{65} - 30 q^{66} - 60 q^{68} + 46 q^{72} + 72 q^{73} - 56 q^{74} - 8 q^{78} - 42 q^{80} - 192 q^{81} + 90 q^{82} + 22 q^{86} - 24 q^{88} + 120 q^{89} - 92 q^{92} - 8 q^{93} + 54 q^{94} + 42 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)