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Properties

Label 483.3.bd
Level $483$
Weight $3$
Character orbit 483.bd
Rep. character $\chi_{483}(37,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1280$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.bd (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(483, [\chi])\).

Total New Old
Modular forms 2640 1280 1360
Cusp forms 2480 1280 1200
Eisenstein series 160 0 160

Trace form

\( 1280 q - 4 q^{2} + 116 q^{4} - 8 q^{8} + 192 q^{9} + O(q^{10}) \) \( 1280 q - 4 q^{2} + 116 q^{4} - 8 q^{8} + 192 q^{9} + 476 q^{16} - 12 q^{18} + 352 q^{20} - 40 q^{23} - 424 q^{25} + 84 q^{26} + 1056 q^{28} - 136 q^{29} - 12 q^{31} - 368 q^{32} + 96 q^{35} - 1092 q^{36} + 352 q^{37} + 1540 q^{38} + 208 q^{41} + 330 q^{42} - 176 q^{43} + 154 q^{44} - 92 q^{46} + 52 q^{47} - 288 q^{48} + 448 q^{49} + 1444 q^{50} - 264 q^{51} - 1368 q^{52} + 192 q^{55} - 1210 q^{56} + 1056 q^{57} - 766 q^{58} - 804 q^{59} + 616 q^{61} + 912 q^{62} - 1176 q^{64} + 168 q^{69} - 264 q^{70} - 176 q^{71} + 12 q^{72} + 48 q^{73} + 374 q^{74} + 96 q^{75} + 296 q^{77} - 96 q^{78} + 484 q^{79} - 2178 q^{80} + 576 q^{81} - 1464 q^{82} + 1928 q^{85} + 36 q^{87} + 990 q^{88} + 484 q^{92} + 144 q^{93} + 262 q^{94} - 702 q^{95} + 300 q^{96} + 1648 q^{98} + 660 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)