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Properties

Label 115.4.j
Level $115$
Weight $4$
Character orbit 115.j
Rep. character $\chi_{115}(4,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $340$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 115.j (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(115, [\chi])\).

Total New Old
Modular forms 380 380 0
Cusp forms 340 340 0
Eisenstein series 40 40 0

Trace form

\( 340 q + 122 q^{4} - 25 q^{5} - 46 q^{6} + 288 q^{9} + O(q^{10}) \) \( 340 q + 122 q^{4} - 25 q^{5} - 46 q^{6} + 288 q^{9} - 25 q^{10} - 14 q^{11} - 258 q^{14} + 363 q^{15} - 462 q^{16} - 166 q^{19} - 535 q^{20} + 10 q^{21} - 152 q^{24} - 497 q^{25} + 122 q^{26} - 78 q^{29} + 1779 q^{30} + 58 q^{31} + 1628 q^{34} - 127 q^{35} - 1886 q^{36} + 1046 q^{39} - 661 q^{40} - 290 q^{41} - 3910 q^{44} + 1324 q^{45} - 206 q^{46} - 726 q^{49} - 131 q^{50} + 1082 q^{51} + 3914 q^{54} + 1337 q^{55} - 3530 q^{56} + 4668 q^{59} + 945 q^{60} - 594 q^{61} - 4346 q^{64} - 5487 q^{65} + 7444 q^{66} - 6950 q^{69} - 6974 q^{70} + 5438 q^{71} - 4954 q^{74} - 7913 q^{75} + 17316 q^{76} - 2142 q^{79} + 428 q^{80} - 3792 q^{81} + 13278 q^{84} + 9743 q^{85} - 12530 q^{86} - 1218 q^{89} + 15918 q^{90} - 15516 q^{91} + 2494 q^{94} + 95 q^{95} - 44100 q^{96} - 10066 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.4.j.a 115.j 115.j $340$ $6.785$ None \(0\) \(0\) \(-25\) \(0\) $\mathrm{SU}(2)[C_{22}]$