Properties

Label 57.3.c
Level $57$
Weight $3$
Character orbit 57.c
Rep. character $\chi_{57}(37,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 57.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(57, [\chi])\).

Total New Old
Modular forms 16 6 10
Cusp forms 12 6 6
Eisenstein series 4 0 4

Trace form

\( 6q - 4q^{4} - 2q^{5} - 12q^{6} + 14q^{7} - 18q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 2q^{5} - 12q^{6} + 14q^{7} - 18q^{9} + 6q^{11} - 44q^{16} + 14q^{17} + 38q^{19} + 80q^{20} + 12q^{23} + 12q^{24} - 36q^{25} + 16q^{26} - 128q^{28} + 48q^{30} - 222q^{35} + 12q^{36} + 152q^{38} + 24q^{39} - 48q^{42} + 14q^{43} - 16q^{44} + 6q^{45} - 74q^{47} + 252q^{49} + 36q^{54} + 58q^{55} + 256q^{58} - 90q^{61} - 256q^{62} - 42q^{63} - 44q^{64} - 96q^{66} - 256q^{68} + 70q^{73} + 336q^{74} - 76q^{76} - 262q^{77} + 24q^{80} + 54q^{81} - 16q^{82} + 204q^{83} - 190q^{85} + 240q^{87} - 232q^{92} - 72q^{93} + 38q^{95} + 204q^{96} - 18q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(57, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
57.3.c.a \(2\) \(1.553\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(8\) \(-20\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+q^{4}+4q^{5}-3q^{6}+\cdots\)
57.3.c.b \(4\) \(1.553\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-10\) \(34\) \(q+(-\beta _{1}-\beta _{3})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(57, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)