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Properties

Label 1764.2.by
Level $1764$
Weight $2$
Character orbit 1764.by
Rep. character $\chi_{1764}(85,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $672$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.by (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).

Total New Old
Modular forms 4104 672 3432
Cusp forms 3960 672 3288
Eisenstein series 144 0 144

Trace form

\( 672 q + 4 q^{5} - q^{7} - 10 q^{9} + O(q^{10}) \) \( 672 q + 4 q^{5} - q^{7} - 10 q^{9} - 2 q^{13} - 6 q^{15} - 28 q^{17} + 4 q^{19} - q^{21} - 15 q^{23} + 56 q^{25} + 21 q^{27} + 10 q^{29} + 4 q^{31} + 10 q^{33} + 14 q^{35} - 10 q^{37} + 32 q^{39} + 4 q^{43} - 29 q^{45} + 30 q^{47} - 7 q^{49} + 24 q^{51} - 84 q^{53} + 60 q^{55} - 24 q^{57} + 22 q^{59} + 23 q^{61} + 3 q^{63} + 14 q^{65} - 14 q^{67} + 42 q^{69} + 62 q^{71} + 28 q^{73} + 20 q^{75} - 11 q^{77} + 10 q^{79} - 46 q^{81} + 82 q^{83} + 30 q^{87} + 10 q^{89} + 10 q^{91} + 157 q^{93} - 44 q^{95} - 2 q^{97} - 226 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)