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Properties

Label 1764.2.cr
Level $1764$
Weight $2$
Character orbit 1764.cr
Rep. character $\chi_{1764}(5,\cdot)$
Character field $\Q(\zeta_{42})$
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.cr (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 672 q + q^{7} + 10 q^{9} + O(q^{10}) \) \( 672 q + q^{7} + 10 q^{9} + 3 q^{13} - 3 q^{15} - 9 q^{17} - 6 q^{21} - 9 q^{23} + 56 q^{25} - 51 q^{27} - 6 q^{29} + 15 q^{35} + 13 q^{37} - 11 q^{39} + 6 q^{41} + 2 q^{43} - 152 q^{45} - 90 q^{47} + 5 q^{49} + 15 q^{51} + 12 q^{53} - 42 q^{55} + 2 q^{57} + 30 q^{59} - 49 q^{61} + 15 q^{63} - 14 q^{67} - 49 q^{69} - 63 q^{71} + 15 q^{75} - 3 q^{77} - 14 q^{79} + 2 q^{81} + 8 q^{87} + 84 q^{89} - 9 q^{91} - 128 q^{93} + 3 q^{97} - 79 q^{99} + O(q^{100}) \)

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

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