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Properties

Label 483.3.k
Level $483$
Weight $3$
Character orbit 483.k
Rep. character $\chi_{483}(208,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

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

Total New Old
Modular forms 264 116 148
Cusp forms 248 116 132
Eisenstein series 16 0 16

Trace form

\( 116 q + 6 q^{3} - 112 q^{4} + 14 q^{7} - 24 q^{8} + 174 q^{9} + O(q^{10}) \) \( 116 q + 6 q^{3} - 112 q^{4} + 14 q^{7} - 24 q^{8} + 174 q^{9} + 60 q^{10} - 48 q^{12} - 76 q^{14} + 48 q^{15} - 256 q^{16} - 96 q^{17} + 78 q^{19} + 72 q^{21} + 8 q^{22} + 108 q^{24} + 294 q^{25} - 32 q^{28} - 136 q^{29} + 102 q^{31} + 48 q^{32} - 216 q^{33} + 52 q^{35} - 672 q^{36} - 86 q^{37} - 156 q^{38} - 18 q^{39} - 144 q^{40} + 60 q^{42} + 68 q^{43} + 176 q^{44} + 600 q^{47} - 106 q^{49} + 184 q^{50} - 492 q^{52} + 136 q^{53} + 280 q^{56} - 12 q^{57} - 236 q^{58} - 516 q^{59} - 216 q^{60} - 612 q^{61} - 6 q^{63} + 1232 q^{64} + 404 q^{65} + 216 q^{66} - 122 q^{67} + 708 q^{68} - 740 q^{70} - 312 q^{71} - 36 q^{72} + 378 q^{73} - 444 q^{74} + 210 q^{75} + 328 q^{77} - 696 q^{78} - 230 q^{79} + 1572 q^{80} - 522 q^{81} - 288 q^{82} + 312 q^{84} + 232 q^{85} + 228 q^{86} - 216 q^{87} + 612 q^{88} + 72 q^{89} - 814 q^{91} + 234 q^{93} - 372 q^{94} + 464 q^{95} - 432 q^{96} + 640 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)