Properties

Label 2156.2.bi
Level $2156$
Weight $2$
Character orbit 2156.bi
Rep. character $\chi_{2156}(117,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $320$
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.bi (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2880 320 2560
Cusp forms 2496 320 2176
Eisenstein series 384 0 384

Trace form

\( 320 q + 6 q^{5} - 28 q^{9} + O(q^{10}) \) \( 320 q + 6 q^{5} - 28 q^{9} - 3 q^{11} - 36 q^{15} + 30 q^{17} - 2 q^{23} - 22 q^{25} - 20 q^{29} + 18 q^{31} - 54 q^{33} - 6 q^{37} - 40 q^{39} - 18 q^{45} - 12 q^{47} + 20 q^{51} + 28 q^{53} + 80 q^{57} - 30 q^{59} + 15 q^{61} + 24 q^{67} + 52 q^{71} + 45 q^{73} + 126 q^{75} + 15 q^{79} + 104 q^{81} + 210 q^{85} + 18 q^{89} + q^{93} - 75 q^{95} + 116 q^{99} + O(q^{100}) \)

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

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