↑

Properties

Label 2156.2.r
Level $2156$
Weight $2$
Character orbit 2156.r
Rep. character $\chi_{2156}(309,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $288$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2156.r (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2052 288 1764
Cusp forms 1980 288 1692
Eisenstein series 72 0 72

Trace form

\( 288 q + 4 q^{5} - 2 q^{7} - 72 q^{9} + O(q^{10}) \) \( 288 q + 4 q^{5} - 2 q^{7} - 72 q^{9} - 4 q^{13} - 12 q^{15} - 12 q^{17} - 12 q^{19} - 2 q^{21} - 56 q^{25} + 12 q^{27} - 28 q^{29} - 8 q^{31} + 4 q^{33} + 10 q^{35} + 38 q^{37} + 64 q^{39} + 28 q^{41} + 16 q^{43} + 8 q^{45} - 50 q^{47} + 4 q^{49} + 24 q^{51} + 10 q^{53} + 22 q^{57} + 44 q^{59} + 84 q^{61} + 46 q^{63} - 28 q^{65} - 12 q^{67} + 12 q^{69} + 22 q^{71} + 16 q^{73} - 132 q^{75} - 2 q^{77} + 4 q^{79} - 60 q^{81} + 46 q^{83} - 112 q^{85} - 12 q^{87} + 12 q^{89} - 60 q^{91} - 58 q^{93} + 8 q^{95} - 68 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)