Properties

Label 115.5.h
Level $115$
Weight $5$
Character orbit 115.h
Rep. character $\chi_{115}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 115.h (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(115, [\chi])\).

Total New Old
Modular forms 500 320 180
Cusp forms 460 320 140
Eisenstein series 40 0 40

Trace form

\( 320 q - 12 q^{2} - 272 q^{4} + 166 q^{6} - 246 q^{8} - 896 q^{9} + O(q^{10}) \) \( 320 q - 12 q^{2} - 272 q^{4} + 166 q^{6} - 246 q^{8} - 896 q^{9} + 30 q^{12} - 204 q^{13} - 2264 q^{16} + 990 q^{17} - 50 q^{18} + 1914 q^{19} + 2706 q^{21} + 258 q^{23} - 7260 q^{24} + 4000 q^{25} - 8922 q^{26} - 6642 q^{27} + 888 q^{29} + 3844 q^{31} + 10512 q^{32} - 12826 q^{34} - 5850 q^{35} - 11920 q^{36} + 20790 q^{38} + 5044 q^{39} + 24200 q^{40} + 10530 q^{41} + 14432 q^{43} + 1914 q^{44} - 9812 q^{46} + 10272 q^{47} - 55958 q^{48} - 16022 q^{49} - 6750 q^{50} - 34848 q^{51} + 7966 q^{52} - 14784 q^{53} - 42582 q^{54} - 7000 q^{55} - 14454 q^{56} - 5082 q^{57} + 92648 q^{58} + 12330 q^{59} + 34650 q^{60} + 22484 q^{61} + 70986 q^{62} + 55550 q^{63} + 20882 q^{64} + 22528 q^{66} + 5852 q^{67} + 17060 q^{69} + 4800 q^{70} - 42486 q^{71} - 180818 q^{72} - 11284 q^{73} - 111870 q^{74} - 61952 q^{76} - 72522 q^{77} - 72762 q^{78} - 3124 q^{79} + 12332 q^{81} + 83702 q^{82} + 130218 q^{83} + 349492 q^{84} + 12850 q^{85} + 60192 q^{86} + 146516 q^{87} + 88176 q^{88} + 45936 q^{89} + 5790 q^{92} - 36668 q^{93} - 182364 q^{94} - 10800 q^{95} - 67282 q^{96} - 125136 q^{97} - 67860 q^{98} - 283008 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.5.h.a 115.h 23.d $320$ $11.888$ None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{5}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)