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Properties

Label 168.4.p
Level $168$
Weight $4$
Character orbit 168.p
Rep. character $\chi_{168}(139,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 168.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(168, [\chi])\).

Total New Old
Modular forms 100 48 52
Cusp forms 92 48 44
Eisenstein series 8 0 8

Trace form

\( 48 q - 2 q^{2} + 10 q^{4} + 118 q^{8} - 432 q^{9} + O(q^{10}) \) \( 48 q - 2 q^{2} + 10 q^{4} + 118 q^{8} - 432 q^{9} - 40 q^{11} + 38 q^{14} - 142 q^{16} + 18 q^{18} - 376 q^{22} + 1200 q^{25} - 274 q^{28} + 336 q^{30} + 318 q^{32} - 456 q^{35} - 90 q^{36} + 564 q^{42} - 808 q^{43} + 1584 q^{44} - 388 q^{46} + 360 q^{49} - 14 q^{50} + 226 q^{56} + 336 q^{57} - 3176 q^{58} - 192 q^{60} + 1954 q^{64} - 4104 q^{67} - 648 q^{70} - 1062 q^{72} + 2384 q^{74} - 1800 q^{78} + 3888 q^{81} + 264 q^{84} - 880 q^{86} + 4184 q^{88} + 104 q^{91} + 2044 q^{92} - 6018 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(168, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
168.4.p.a 168.p 56.e $48$ $9.912$ None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)