Properties

Label 456.2.f
Level $456$
Weight $2$
Character orbit 456.f
Rep. character $\chi_{456}(113,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(29\)

Dimensions

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

Total New Old
Modular forms 88 20 68
Cusp forms 72 20 52
Eisenstein series 16 0 16

Trace form

\( 20 q - 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{7} + 6 q^{9} + 4 q^{19} - 28 q^{25} + 14 q^{39} + 40 q^{43} - 4 q^{45} + 32 q^{49} - 24 q^{55} - 2 q^{57} - 8 q^{61} - 34 q^{63} - 52 q^{73} + 46 q^{81} - 16 q^{85} + 26 q^{87} - 36 q^{93} + 4 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
456.2.f.a 456.f 57.d $10$ $3.641$ 10.0.\(\cdots\).1 None \(0\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots\)
456.2.f.b 456.f 57.d $10$ $3.641$ 10.0.\(\cdots\).1 None \(0\) \(1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots\)

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

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