Properties

Label 456.2.bf
Level $456$
Weight $2$
Character orbit 456.bf
Rep. character $\chi_{456}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $4$
Sturm bound $160$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(456, [\chi])\).

Total New Old
Modular forms 176 40 136
Cusp forms 144 40 104
Eisenstein series 32 0 32

Trace form

\( 40q + 3q^{3} + 4q^{7} + 3q^{9} + O(q^{10}) \) \( 40q + 3q^{3} + 4q^{7} + 3q^{9} - 6q^{13} + 12q^{15} - 10q^{19} + 16q^{25} + 9q^{33} + 4q^{39} + 2q^{43} + 40q^{45} + 28q^{49} - 18q^{51} - 12q^{55} - 22q^{57} + 2q^{61} - 20q^{63} - 12q^{67} + 4q^{73} - 54q^{79} - 13q^{81} + 4q^{85} - 8q^{87} - 90q^{91} - 18q^{93} - 66q^{97} - 25q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(456, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
456.2.bf.a \(4\) \(3.641\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(-3\) \(2\) \(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
456.2.bf.b \(4\) \(3.641\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(2\) \(3\) \(2\) \(q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots\)
456.2.bf.c \(16\) \(3.641\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-1\) \(-3\) \(0\) \(q-\beta _{1}q^{3}-\beta _{14}q^{5}+(\beta _{5}-\beta _{13})q^{7}+\cdots\)
456.2.bf.d \(16\) \(3.641\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(1\) \(3\) \(0\) \(q+\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(\beta _{5}-\beta _{13}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)