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Properties

Label 2156.2.x
Level $2156$
Weight $2$
Character orbit 2156.x
Rep. character $\chi_{2156}(293,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1440 160 1280
Cusp forms 1248 160 1088
Eisenstein series 192 0 192

Trace form

\( 160 q + 28 q^{9} + O(q^{10}) \) \( 160 q + 28 q^{9} + 6 q^{11} - 4 q^{23} + 4 q^{25} + 20 q^{29} + 36 q^{37} + 40 q^{39} - 80 q^{51} + 56 q^{53} - 80 q^{57} + 96 q^{67} - 28 q^{71} + 30 q^{79} + 4 q^{81} + 30 q^{85} + 26 q^{93} + 90 q^{95} - 20 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)