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Properties

Label 2156.2.bg
Level $2156$
Weight $2$
Character orbit 2156.bg
Rep. character $\chi_{2156}(361,\cdot)$
Character field $\Q(\zeta_{15})$
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.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 320 q - 2 q^{5} + 28 q^{9} + O(q^{10}) \) \( 320 q - 2 q^{5} + 28 q^{9} + 5 q^{11} + 8 q^{13} + 36 q^{15} - 20 q^{17} - 2 q^{23} + 66 q^{25} - 18 q^{27} - 4 q^{29} - 6 q^{31} + 32 q^{33} - 18 q^{37} + 22 q^{39} + 38 q^{41} + 20 q^{43} + 26 q^{45} - 22 q^{47} + 38 q^{51} - 20 q^{53} + 2 q^{55} + 100 q^{57} - 14 q^{59} - 29 q^{61} + 64 q^{65} - 8 q^{67} + 52 q^{69} + 140 q^{71} + 3 q^{73} + 22 q^{75} + 41 q^{79} + 48 q^{81} + 64 q^{83} - 54 q^{85} + 104 q^{87} + 10 q^{89} + 49 q^{93} - 29 q^{95} + 48 q^{97} - 172 q^{99} + O(q^{100}) \)

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

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