Properties

Label 216.3.h
Level $216$
Weight $3$
Character orbit 216.h
Rep. character $\chi_{216}(53,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $6$
Sturm bound $108$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(108\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(216, [\chi])\).

Total New Old
Modular forms 78 32 46
Cusp forms 66 32 34
Eisenstein series 12 0 12

Trace form

\( 32q - 2q^{4} + O(q^{10}) \) \( 32q - 2q^{4} - 14q^{10} + 18q^{16} - 46q^{22} + 160q^{25} + 74q^{28} + 64q^{31} - 88q^{34} + 30q^{40} - 256q^{46} + 240q^{49} - 124q^{52} - 128q^{55} - 364q^{58} - 182q^{64} + 102q^{70} + 80q^{73} - 116q^{76} - 384q^{79} + 472q^{82} + 398q^{88} - 72q^{94} + 96q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
216.3.h.a \(2\) \(5.886\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-6}) \) \(-4\) \(0\) \(-2\) \(10\) \(q-2q^{2}+4q^{4}+(-1+\beta )q^{5}+(5+\beta )q^{7}+\cdots\)
216.3.h.b \(2\) \(5.886\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-6}) \) \(4\) \(0\) \(2\) \(10\) \(q+2q^{2}+4q^{4}+(1+\beta )q^{5}+(5-\beta )q^{7}+\cdots\)
216.3.h.c \(6\) \(5.886\) 6.0.121670000.1 None \(-1\) \(0\) \(-2\) \(-10\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
216.3.h.d \(6\) \(5.886\) 6.0.121670000.1 None \(1\) \(0\) \(2\) \(-10\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
216.3.h.e \(8\) \(5.886\) 8.0.629407744.1 None \(0\) \(0\) \(0\) \(-48\) \(q+\beta _{1}q^{2}+(-1+\beta _{5}+\beta _{7})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
216.3.h.f \(8\) \(5.886\) 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(48\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{5})q^{5}+(6+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)