Properties

Label 115.4.g
Level $115$
Weight $4$
Character orbit 115.g
Rep. character $\chi_{115}(6,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $240$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 115.g (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 380 240 140
Cusp forms 340 240 100
Eisenstein series 40 0 40

Trace form

\( 240 q + 4 q^{2} - 104 q^{4} + 10 q^{5} + 26 q^{6} + 28 q^{7} - 42 q^{8} - 244 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{2} - 104 q^{4} + 10 q^{5} + 26 q^{6} + 28 q^{7} - 42 q^{8} - 244 q^{9} - 40 q^{10} + 28 q^{11} - 78 q^{12} + 16 q^{13} - 236 q^{14} + 60 q^{15} + 600 q^{16} + 344 q^{17} + 218 q^{18} - 224 q^{19} + 120 q^{20} - 968 q^{21} - 1176 q^{22} - 60 q^{23} - 2628 q^{24} - 600 q^{25} - 502 q^{26} + 336 q^{27} + 184 q^{28} + 972 q^{29} - 160 q^{30} + 856 q^{31} + 2440 q^{32} - 328 q^{33} + 2718 q^{34} + 1190 q^{35} + 4172 q^{36} + 324 q^{37} + 2670 q^{38} + 616 q^{39} - 1320 q^{40} - 1428 q^{41} + 808 q^{42} - 3272 q^{43} - 618 q^{44} - 3200 q^{45} - 8232 q^{46} - 368 q^{47} - 7006 q^{48} - 2722 q^{49} - 450 q^{50} - 1512 q^{51} + 2038 q^{52} - 936 q^{53} + 6486 q^{54} + 1860 q^{55} + 8414 q^{56} + 6528 q^{57} + 13308 q^{58} + 2826 q^{59} + 3450 q^{60} + 1372 q^{61} - 2626 q^{62} - 4096 q^{63} - 4318 q^{64} + 260 q^{65} - 5988 q^{66} - 960 q^{67} - 13728 q^{68} + 156 q^{69} - 360 q^{70} - 1028 q^{71} - 8946 q^{72} - 1992 q^{73} + 3946 q^{74} - 3748 q^{76} + 9744 q^{77} + 20910 q^{78} + 4672 q^{79} + 2000 q^{80} - 544 q^{81} + 8138 q^{82} + 7876 q^{83} + 10772 q^{84} - 520 q^{85} + 5284 q^{86} - 20612 q^{87} - 16276 q^{88} - 10524 q^{89} - 1420 q^{90} - 720 q^{91} - 18498 q^{92} - 26080 q^{93} - 14408 q^{94} - 480 q^{95} + 14174 q^{96} - 6628 q^{97} - 4308 q^{98} - 9980 q^{99} + O(q^{100}) \)

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.g.a 115.g 23.c $110$ $6.785$ None \(-2\) \(6\) \(-55\) \(-10\) $\mathrm{SU}(2)[C_{11}]$
115.4.g.b 115.g 23.c $130$ $6.785$ None \(6\) \(-6\) \(65\) \(38\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)