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Properties

Label 169.4.k
Level $169$
Weight $4$
Character orbit 169.k
Rep. character $\chi_{169}(4,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $1056$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.k (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(169, [\chi])\).

Total New Old
Modular forms 1104 1104 0
Cusp forms 1056 1056 0
Eisenstein series 48 48 0

Trace form

\( 1056 q - 23 q^{2} - 31 q^{3} - 193 q^{4} - 26 q^{5} + 22 q^{6} - 41 q^{7} - 26 q^{8} + 351 q^{9} + O(q^{10}) \) \( 1056 q - 23 q^{2} - 31 q^{3} - 193 q^{4} - 26 q^{5} + 22 q^{6} - 41 q^{7} - 26 q^{8} + 351 q^{9} - 41 q^{10} - 11 q^{11} - 126 q^{12} + 559 q^{13} + 218 q^{14} + 372 q^{15} + 603 q^{16} + 120 q^{17} + 2392 q^{18} + 312 q^{19} + 85 q^{20} - 26 q^{21} + 593 q^{22} - 1784 q^{23} - 1832 q^{24} + 1900 q^{25} - 377 q^{26} + 380 q^{27} - 302 q^{28} - 174 q^{29} - 2104 q^{30} + 1378 q^{31} - 190 q^{32} + 295 q^{33} + 1599 q^{34} - 328 q^{35} - 1391 q^{36} + 292 q^{37} + 37 q^{38} + 2821 q^{39} + 4732 q^{40} + 184 q^{41} - 8146 q^{42} + 133 q^{43} + 78 q^{44} - 3483 q^{45} - 498 q^{46} + 156 q^{47} - 4269 q^{48} - 1081 q^{49} - 794 q^{50} + 1826 q^{51} + 2353 q^{52} + 4205 q^{53} + 2044 q^{54} - 7430 q^{55} - 660 q^{56} - 2873 q^{57} - 347 q^{58} - 8445 q^{59} - 2522 q^{60} - 96 q^{61} + 3937 q^{62} + 5154 q^{63} + 6008 q^{64} + 1183 q^{65} + 17813 q^{66} - 7217 q^{67} - 6396 q^{68} + 146 q^{69} - 8327 q^{71} + 6492 q^{72} - 26 q^{73} - 2813 q^{74} + 8477 q^{75} + 2820 q^{76} + 1276 q^{77} - 8138 q^{78} - 410 q^{79} - 1962 q^{80} + 2374 q^{81} - 9827 q^{82} - 12246 q^{83} + 13695 q^{84} - 7694 q^{85} + 1066 q^{86} - 6261 q^{87} - 13146 q^{88} + 1122 q^{89} + 1508 q^{90} + 3575 q^{91} + 442 q^{92} + 17724 q^{93} + 7706 q^{94} + 2435 q^{95} + 4199 q^{96} + 1153 q^{97} + 1411 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(169, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
169.4.k.a 169.k 169.k $1056$ $9.971$ None 169.4.k.a \(-23\) \(-31\) \(-26\) \(-41\) $\mathrm{SU}(2)[C_{78}]$