Properties

Label 228.3.g
Level $228$
Weight $3$
Character orbit 228.g
Rep. character $\chi_{228}(115,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 228.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).

Total New Old
Modular forms 84 36 48
Cusp forms 76 36 40
Eisenstein series 8 0 8

Trace form

\( 36 q + 4 q^{2} + 12 q^{4} + 8 q^{5} - 20 q^{8} - 108 q^{9} + O(q^{10}) \) \( 36 q + 4 q^{2} + 12 q^{4} + 8 q^{5} - 20 q^{8} - 108 q^{9} + 8 q^{10} + 24 q^{12} - 24 q^{13} - 12 q^{14} + 4 q^{16} - 40 q^{17} - 12 q^{18} - 80 q^{20} + 12 q^{22} + 36 q^{24} + 284 q^{25} - 112 q^{26} - 48 q^{28} + 104 q^{29} + 24 q^{30} + 44 q^{32} + 48 q^{33} + 140 q^{34} - 36 q^{36} - 184 q^{37} + 180 q^{40} - 200 q^{41} + 48 q^{42} + 96 q^{44} - 24 q^{45} - 28 q^{46} - 144 q^{48} - 332 q^{49} + 176 q^{50} + 276 q^{52} + 264 q^{53} - 192 q^{56} - 184 q^{58} - 180 q^{60} + 40 q^{61} - 240 q^{62} - 372 q^{64} + 176 q^{65} - 120 q^{66} - 104 q^{68} - 60 q^{70} + 60 q^{72} + 424 q^{73} - 104 q^{74} - 400 q^{77} - 180 q^{78} + 704 q^{80} + 324 q^{81} + 528 q^{82} + 312 q^{84} - 128 q^{85} + 668 q^{86} - 496 q^{88} - 520 q^{89} - 24 q^{90} - 456 q^{92} - 32 q^{94} + 300 q^{96} - 440 q^{97} - 472 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.3.g.a $36$ $6.213$ None \(4\) \(0\) \(8\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)