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Properties

Label 1722.2.by
Level $1722$
Weight $2$
Character orbit 1722.by
Rep. character $\chi_{1722}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $896$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1722 = 2 \cdot 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1722.by (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 861 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2752 896 1856
Cusp forms 2624 896 1728
Eisenstein series 128 0 128

Trace form

\( 896 q - 112 q^{4} + 4 q^{9} + O(q^{10}) \) \( 896 q - 112 q^{4} + 4 q^{9} - 24 q^{15} + 112 q^{16} - 38 q^{21} + 24 q^{22} + 18 q^{24} + 104 q^{25} + 6 q^{30} - 90 q^{33} + 8 q^{36} + 20 q^{37} + 20 q^{39} + 32 q^{42} - 16 q^{43} + 24 q^{45} + 24 q^{46} + 32 q^{49} - 6 q^{51} + 8 q^{57} + 16 q^{58} + 18 q^{60} - 108 q^{61} - 16 q^{63} + 224 q^{64} - 24 q^{66} - 36 q^{67} + 8 q^{70} + 54 q^{75} - 16 q^{78} + 16 q^{79} + 76 q^{81} + 24 q^{82} + 14 q^{84} - 24 q^{87} + 12 q^{88} - 64 q^{91} + 24 q^{93} + 96 q^{94} - 12 q^{96} + 184 q^{99} + O(q^{100}) \)

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

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