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Properties

Label 1764.3.cd
Level $1764$
Weight $3$
Character orbit 1764.cd
Rep. character $\chi_{1764}(53,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $456$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.cd (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1764, [\chi])\).

Total New Old
Modular forms 8208 456 7752
Cusp forms 7920 456 7464
Eisenstein series 288 0 288

Trace form

\( 456 q + 2 q^{7} + O(q^{10}) \) \( 456 q + 2 q^{7} + 20 q^{13} + 6 q^{19} - 202 q^{25} - 118 q^{31} - 20 q^{37} - 140 q^{43} + 158 q^{49} + 64 q^{55} - 802 q^{61} + 110 q^{67} - 254 q^{73} - 298 q^{79} + 512 q^{85} + 786 q^{91} + 712 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)