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Properties

Label 1764.2.cb
Level $1764$
Weight $2$
Character orbit 1764.cb
Rep. character $\chi_{1764}(173,\cdot)$
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.cb (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

\( 672 q + q^{7} - 26 q^{9} + O(q^{10}) \) \( 672 q + q^{7} - 26 q^{9} - 3 q^{13} - 3 q^{15} + 9 q^{17} - 63 q^{23} - 112 q^{25} + 30 q^{27} + 36 q^{29} - 6 q^{31} + 27 q^{33} - 15 q^{35} + 13 q^{37} + 7 q^{39} - 6 q^{41} + 2 q^{43} + 106 q^{45} + 18 q^{47} - 13 q^{49} - 3 q^{51} - 12 q^{53} - 42 q^{55} + 2 q^{57} + 15 q^{59} + 95 q^{61} + 9 q^{63} + 21 q^{65} + 7 q^{67} - 7 q^{69} + 63 q^{71} + 99 q^{75} + 45 q^{77} + 7 q^{79} + 74 q^{81} + 59 q^{87} - 84 q^{89} - 9 q^{91} - 233 q^{93} + 18 q^{95} - 3 q^{97} - 79 q^{99} + O(q^{100}) \)

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

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