Properties

Label 2156.2.cl
Level $2156$
Weight $2$
Character orbit 2156.cl
Rep. character $\chi_{2156}(17,\cdot)$
Character field $\Q(\zeta_{210})$
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.cl (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{210})\)
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

\( 2688 q + 6 q^{5} - 5 q^{7} + 56 q^{9} + O(q^{10}) \) \( 2688 q + 6 q^{5} - 5 q^{7} + 56 q^{9} - 6 q^{11} + 30 q^{15} - 5 q^{17} - 44 q^{23} + 50 q^{25} + 63 q^{27} - 20 q^{29} + 18 q^{31} - 54 q^{33} + 45 q^{35} + 10 q^{37} - 116 q^{45} - 47 q^{47} + 103 q^{49} + 260 q^{51} + 70 q^{53} - 105 q^{55} + 80 q^{57} - 58 q^{59} + 15 q^{61} - 35 q^{63} + 40 q^{67} - 56 q^{69} + 36 q^{71} - 60 q^{73} + 126 q^{75} - 4 q^{77} + 15 q^{79} - 188 q^{81} + 50 q^{85} + 18 q^{89} + 166 q^{91} + 9 q^{93} + 5 q^{95} - 396 q^{99} + O(q^{100}) \)

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

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