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Properties

Label 2156.2.ce
Level $2156$
Weight $2$
Character orbit 2156.ce
Rep. character $\chi_{2156}(9,\cdot)$
Character field $\Q(\zeta_{105})$
Dimension $2688$
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.ce (of order \(105\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{105})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 16416 2688 13728
Cusp forms 15840 2688 13152
Eisenstein series 576 0 576

Trace form

\( 2688 q - 2 q^{5} - 7 q^{7} - 56 q^{9} + O(q^{10}) \) \( 2688 q - 2 q^{5} - 7 q^{7} - 56 q^{9} - 6 q^{11} + 8 q^{13} - 30 q^{15} + q^{17} + 28 q^{19} - 20 q^{21} - 44 q^{23} - 54 q^{25} + 45 q^{27} + 12 q^{29} - 6 q^{31} + 32 q^{33} - 13 q^{35} - 2 q^{37} - 10 q^{39} + 38 q^{41} + 20 q^{43} + 208 q^{45} + 69 q^{47} + 71 q^{49} - 162 q^{51} - 62 q^{53} + 107 q^{55} + 68 q^{57} + 14 q^{59} - 29 q^{61} + 79 q^{63} + 40 q^{65} - 24 q^{67} + 108 q^{69} + 60 q^{71} + 66 q^{73} + 22 q^{75} + 60 q^{77} + 17 q^{79} + 124 q^{81} + 22 q^{83} - 38 q^{85} - 92 q^{87} - 214 q^{89} + 110 q^{91} + 9 q^{93} - 221 q^{95} - 204 q^{97} + 372 q^{99} + O(q^{100}) \)

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

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