↑

Properties

Label 1722.2.ck
Level $1722$
Weight $2$
Character orbit 1722.ck
Rep. character $\chi_{1722}(11,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $3584$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1722 = 2 \cdot 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1722.ck (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1722, [\chi])\).

Total New Old
Modular forms 11008 3584 7424
Cusp forms 10496 3584 6912
Eisenstein series 512 0 512

Trace form

\( 3584 q - 8 q^{9} + O(q^{10}) \) \( 3584 q - 8 q^{9} - 48 q^{15} - 448 q^{16} - 32 q^{21} - 32 q^{22} + 8 q^{24} - 32 q^{30} + 152 q^{33} - 16 q^{36} + 128 q^{42} - 32 q^{43} + 16 q^{46} + 48 q^{49} - 72 q^{51} + 64 q^{54} - 64 q^{55} - 32 q^{57} - 64 q^{61} - 160 q^{63} - 16 q^{67} + 48 q^{70} - 16 q^{75} - 32 q^{79} - 16 q^{84} + 8 q^{87} + 64 q^{91} - 80 q^{93} - 96 q^{94} + 128 q^{97} + 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1722, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1722, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1722, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(861, [\chi])\)\(^{\oplus 2}\)