Properties

Label 57.3.h
Level $57$
Weight $3$
Character orbit 57.h
Rep. character $\chi_{57}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
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 32 32 0
Cusp forms 24 24 0
Eisenstein series 8 8 0

Trace form

\( 24 q + q^{3} + 24 q^{4} - 13 q^{6} - 20 q^{7} + 5 q^{9} + O(q^{10}) \) \( 24 q + q^{3} + 24 q^{4} - 13 q^{6} - 20 q^{7} + 5 q^{9} - 28 q^{10} + 30 q^{12} - 22 q^{13} - 14 q^{15} - 36 q^{16} - 78 q^{18} + 18 q^{19} - 40 q^{21} + 22 q^{22} + 111 q^{24} + 68 q^{25} + 4 q^{27} - 82 q^{28} - 248 q^{30} - 44 q^{31} - 59 q^{33} + 128 q^{34} + 53 q^{36} + 100 q^{37} + 144 q^{39} + 300 q^{40} - 32 q^{42} - 234 q^{43} + 304 q^{45} - 128 q^{46} + 357 q^{48} + 52 q^{49} + 14 q^{51} + 166 q^{52} - 202 q^{54} - 24 q^{55} + 168 q^{57} - 184 q^{58} + 26 q^{60} - 14 q^{61} - 228 q^{63} - 624 q^{64} + 283 q^{66} - 252 q^{67} - 228 q^{69} - 312 q^{70} - 429 q^{72} + 144 q^{73} - 406 q^{75} - 180 q^{76} - 478 q^{78} - 110 q^{79} + 437 q^{81} + 434 q^{82} - 192 q^{84} - 420 q^{85} - 384 q^{87} + 1284 q^{88} - 14 q^{90} + 302 q^{91} - 30 q^{93} + 528 q^{94} + 1354 q^{96} + 454 q^{97} + 71 q^{99} + O(q^{100}) \)

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.h.a $8$ $1.553$ 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(48\) \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{6})q^{3}+(\beta _{3}+\beta _{6})q^{4}+\cdots\)
57.3.h.b $16$ $1.553$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(1\) \(0\) \(-68\) \(q-\beta _{3}q^{2}-\beta _{6}q^{3}+(-2\beta _{1}-3\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots\)