Properties

Label 115.3.f
Level $115$
Weight $3$
Character orbit 115.f
Rep. character $\chi_{115}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 115.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(115, [\chi])\).

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

Trace form

\( 44 q - 4 q^{2} - 8 q^{5} - 16 q^{7} + 12 q^{8} + O(q^{10}) \) \( 44 q - 4 q^{2} - 8 q^{5} - 16 q^{7} + 12 q^{8} - 4 q^{10} - 24 q^{11} + 48 q^{12} + 4 q^{13} + 60 q^{15} - 224 q^{16} + 24 q^{17} - 88 q^{18} - 56 q^{20} + 8 q^{21} - 48 q^{22} + 84 q^{25} + 56 q^{26} - 132 q^{27} + 204 q^{28} - 200 q^{30} + 100 q^{31} + 184 q^{32} - 68 q^{33} - 48 q^{35} + 552 q^{36} - 48 q^{37} - 52 q^{38} + 200 q^{40} - 132 q^{41} - 248 q^{42} + 128 q^{43} + 204 q^{45} + 152 q^{47} - 500 q^{48} - 228 q^{50} - 264 q^{51} + 280 q^{52} + 324 q^{53} - 156 q^{55} - 312 q^{56} + 320 q^{57} + 364 q^{58} + 500 q^{60} + 32 q^{61} - 44 q^{62} - 220 q^{63} - 196 q^{65} - 552 q^{66} - 352 q^{67} - 616 q^{68} + 188 q^{70} + 108 q^{71} - 192 q^{72} + 168 q^{73} - 468 q^{75} + 464 q^{76} - 292 q^{77} + 596 q^{78} - 316 q^{80} - 332 q^{81} - 820 q^{82} - 144 q^{83} - 524 q^{85} + 536 q^{86} + 536 q^{87} - 132 q^{88} + 260 q^{90} + 312 q^{91} - 416 q^{93} + 304 q^{95} + 448 q^{96} + 620 q^{97} + 780 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.3.f.a 115.f 5.c $44$ $3.134$ None \(-4\) \(0\) \(-8\) \(-16\) $\mathrm{SU}(2)[C_{4}]$