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Properties

Label 1764.4.j
Level $1764$
Weight $4$
Character orbit 1764.j
Rep. character $\chi_{1764}(589,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $246$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2064 246 1818
Cusp forms 1968 246 1722
Eisenstein series 96 0 96

Trace form

\( 246 q - 3 q^{3} - 14 q^{5} + 3 q^{9} + O(q^{10}) \) \( 246 q - 3 q^{3} - 14 q^{5} + 3 q^{9} + 43 q^{11} - 12 q^{13} + 40 q^{15} + 146 q^{17} + 150 q^{19} + 22 q^{23} - 3003 q^{25} + 252 q^{27} + 12 q^{29} - 12 q^{31} + 157 q^{33} + 240 q^{37} - 208 q^{39} - 651 q^{41} + 213 q^{43} + 94 q^{45} + 654 q^{47} - 187 q^{51} + 1072 q^{53} + 1008 q^{55} + 435 q^{57} - 755 q^{59} + 402 q^{61} + 1198 q^{65} + 375 q^{67} + 70 q^{69} - 1360 q^{71} + 78 q^{73} + 1313 q^{75} - 552 q^{79} + 1439 q^{81} - 1552 q^{83} + 468 q^{85} - 2470 q^{87} + 204 q^{89} + 2410 q^{93} - 36 q^{95} - 435 q^{97} + 1966 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)