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Properties

Label 1764.4.w
Level $1764$
Weight $4$
Character orbit 1764.w
Rep. character $\chi_{1764}(509,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

Total New Old
Modular forms 2064 240 1824
Cusp forms 1968 240 1728
Eisenstein series 96 0 96

Trace form

\( 240 q + 4 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{9} - 24 q^{11} + 36 q^{13} - 174 q^{15} + 72 q^{17} - 186 q^{23} - 3000 q^{25} + 396 q^{27} - 42 q^{29} - 84 q^{37} + 1400 q^{39} + 618 q^{41} + 42 q^{43} - 366 q^{45} - 396 q^{47} + 678 q^{51} + 2148 q^{53} - 536 q^{57} - 1500 q^{59} + 588 q^{67} + 924 q^{69} - 564 q^{75} - 2544 q^{79} - 3924 q^{81} + 720 q^{85} - 2640 q^{87} - 1722 q^{89} + 612 q^{93} + 792 q^{97} - 3574 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)