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Properties

Label 456.2.u
Level $456$
Weight $2$
Character orbit 456.u
Rep. character $\chi_{456}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(41\)

Dimensions

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

Total New Old
Modular forms 168 168 0
Cusp forms 152 152 0
Eisenstein series 16 16 0

Trace form

\( 152 q - 2 q^{3} - 4 q^{4} - 5 q^{6} - 2 q^{9} + O(q^{10}) \) \( 152 q - 2 q^{3} - 4 q^{4} - 5 q^{6} - 2 q^{9} + 8 q^{10} + 2 q^{12} - 4 q^{16} + 6 q^{18} - 16 q^{19} + 2 q^{22} + 3 q^{24} - 64 q^{25} - 8 q^{27} + 6 q^{28} + 4 q^{30} - 4 q^{33} + 8 q^{34} + 25 q^{36} - 40 q^{40} - 18 q^{42} - 4 q^{43} - 16 q^{46} - 19 q^{48} - 136 q^{49} - 14 q^{51} - 26 q^{52} - 2 q^{54} - 2 q^{57} + 64 q^{58} - 18 q^{60} - 112 q^{64} + 9 q^{66} - 4 q^{67} + 72 q^{70} - 29 q^{72} + 4 q^{73} + 136 q^{75} + 32 q^{76} - 50 q^{78} - 6 q^{81} - 54 q^{82} + 36 q^{84} + 68 q^{88} - 22 q^{90} + 24 q^{91} - 8 q^{94} - 98 q^{96} + 12 q^{97} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.u.a 456.u 456.u $4$ $3.641$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
456.2.u.b 456.u 456.u $4$ $3.641$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
456.2.u.c 456.u 456.u $8$ $3.641$ 8.0.4857532416.1 None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{7})q^{2}-\beta _{3}q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots\)
456.2.u.d 456.u 456.u $136$ $3.641$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$