Properties

Label 228.2.c
Level $228$
Weight $2$
Character orbit 228.c
Rep. character $\chi_{228}(191,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 228.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(228, [\chi])\).

Total New Old
Modular forms 44 36 8
Cusp forms 36 36 0
Eisenstein series 8 0 8

Trace form

\( 36q - 6q^{6} + O(q^{10}) \) \( 36q - 6q^{6} + 8q^{10} + 4q^{12} - 8q^{16} + 16q^{18} + 8q^{21} - 12q^{22} - 2q^{24} - 28q^{25} + 12q^{28} - 12q^{30} - 28q^{34} - 22q^{36} - 16q^{37} - 12q^{40} + 10q^{42} + 16q^{45} - 4q^{46} + 32q^{48} - 44q^{49} - 36q^{52} - 20q^{54} - 4q^{58} - 4q^{60} + 16q^{61} + 24q^{64} + 24q^{66} - 16q^{69} + 36q^{70} - 36q^{72} - 8q^{73} - 32q^{78} - 40q^{81} + 72q^{82} - 20q^{84} + 16q^{85} - 16q^{88} - 56q^{90} + 8q^{93} - 56q^{94} + 2q^{96} + 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
228.2.c.a \(36\) \(1.821\) None \(0\) \(0\) \(0\) \(0\)