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Properties

Label 1764.4.l
Level $1764$
Weight $4$
Character orbit 1764.l
Rep. character $\chi_{1764}(949,\cdot)$
Character field $\Q(\zeta_{3})$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 240 1824
Cusp forms 1968 240 1728
Eisenstein series 96 0 96

Trace form

\( 240 q + 40 q^{5} + 18 q^{9} + O(q^{10}) \) \( 240 q + 40 q^{5} + 18 q^{9} + 16 q^{11} + 12 q^{13} + 94 q^{15} - 112 q^{17} - 60 q^{19} + 124 q^{23} + 6000 q^{25} - 402 q^{29} + 30 q^{31} - 380 q^{33} + 84 q^{37} + 470 q^{39} - 210 q^{41} - 42 q^{43} - 386 q^{45} - 66 q^{47} + 1364 q^{51} + 292 q^{53} - 612 q^{55} - 1944 q^{57} - 458 q^{59} - 402 q^{61} + 1264 q^{65} - 294 q^{67} + 28 q^{69} + 2972 q^{71} + 336 q^{73} + 3338 q^{75} - 852 q^{79} + 1430 q^{81} - 1024 q^{83} - 720 q^{85} + 1508 q^{87} - 2922 q^{89} - 2624 q^{93} + 2358 q^{95} + 264 q^{97} + 8314 q^{99} + O(q^{100}) \)

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

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