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Properties

Label 232.4.k
Level $232$
Weight $4$
Character orbit 232.k
Rep. character $\chi_{232}(75,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 232.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 232 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(232, [\chi])\).

Total New Old
Modular forms 184 184 0
Cusp forms 176 176 0
Eisenstein series 8 8 0

Trace form

\( 176 q - 4 q^{2} - 4 q^{3} + 26 q^{8} + O(q^{10}) \) \( 176 q - 4 q^{2} - 4 q^{3} + 26 q^{8} - 18 q^{10} + 36 q^{11} + 130 q^{12} - 56 q^{14} + 296 q^{16} - 56 q^{17} - 266 q^{18} - 4 q^{19} - 260 q^{20} + 176 q^{24} + 3904 q^{25} - 98 q^{26} - 160 q^{27} - 1708 q^{30} + 246 q^{32} + 1272 q^{36} - 830 q^{40} - 240 q^{41} - 812 q^{43} + 2014 q^{44} + 852 q^{46} + 1090 q^{48} - 7456 q^{49} + 278 q^{50} - 296 q^{52} + 2480 q^{54} - 1392 q^{56} + 1028 q^{58} - 8 q^{59} - 1414 q^{60} - 1008 q^{65} + 398 q^{66} - 408 q^{68} - 2520 q^{70} + 568 q^{72} + 736 q^{73} + 5700 q^{74} + 2692 q^{75} - 884 q^{76} + 752 q^{78} - 14136 q^{81} + 1456 q^{82} - 8 q^{83} - 2064 q^{84} + 2548 q^{88} + 1064 q^{89} + 1220 q^{90} + 6332 q^{94} + 576 q^{97} + 2136 q^{98} + 1220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(232, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
232.4.k.a 232.k 232.k $176$ $13.688$ None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$