Properties

Label 95.4.e
Level $95$
Weight $4$
Character orbit 95.e
Rep. character $\chi_{95}(11,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $3$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 95.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(95, [\chi])\).

Total New Old
Modular forms 64 40 24
Cusp forms 56 40 16
Eisenstein series 8 0 8

Trace form

\( 40 q + 4 q^{2} + 2 q^{3} - 86 q^{4} + 26 q^{6} - 40 q^{7} - 96 q^{8} - 210 q^{9} + O(q^{10}) \) \( 40 q + 4 q^{2} + 2 q^{3} - 86 q^{4} + 26 q^{6} - 40 q^{7} - 96 q^{8} - 210 q^{9} + 50 q^{10} - 72 q^{11} + 48 q^{12} + 48 q^{13} + 84 q^{14} + 60 q^{15} - 302 q^{16} - 264 q^{17} - 400 q^{18} + 464 q^{19} + 132 q^{21} + 108 q^{22} + 156 q^{23} + 244 q^{24} - 500 q^{25} + 612 q^{26} + 788 q^{27} + 556 q^{28} - 60 q^{29} - 80 q^{30} - 8 q^{31} + 998 q^{32} + 1430 q^{33} - 1462 q^{34} + 130 q^{35} - 2020 q^{36} - 2096 q^{37} + 1450 q^{38} - 1904 q^{39} + 720 q^{40} - 136 q^{41} - 978 q^{42} - 460 q^{43} - 584 q^{44} + 160 q^{45} + 1988 q^{46} + 696 q^{47} - 1522 q^{48} + 3980 q^{49} - 200 q^{50} + 1360 q^{51} + 850 q^{52} - 392 q^{53} - 458 q^{54} - 2776 q^{56} - 956 q^{57} - 564 q^{58} - 786 q^{59} + 810 q^{60} + 1424 q^{61} - 112 q^{62} + 1032 q^{63} + 4288 q^{64} - 200 q^{65} + 864 q^{66} + 1702 q^{67} + 1260 q^{68} + 1096 q^{69} - 260 q^{70} + 676 q^{71} - 1744 q^{72} - 1162 q^{73} - 4104 q^{74} - 100 q^{75} - 3176 q^{76} - 3888 q^{77} + 4296 q^{78} - 536 q^{79} - 1600 q^{80} + 356 q^{81} + 2270 q^{82} - 3764 q^{83} - 1720 q^{84} + 120 q^{85} + 496 q^{86} + 1760 q^{87} + 1412 q^{88} - 1674 q^{89} + 890 q^{90} - 356 q^{91} - 4088 q^{92} + 156 q^{93} - 2412 q^{94} - 260 q^{95} - 11736 q^{96} - 1790 q^{97} + 12762 q^{98} + 3298 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.4.e.a 95.e 19.c $2$ $5.605$ \(\Q(\sqrt{-3}) \) None \(1\) \(5\) \(-5\) \(44\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}+7\zeta_{6}q^{4}+\cdots\)
95.4.e.b 95.e 19.c $18$ $5.605$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(6\) \(2\) \(-45\) \(-90\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{11}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
95.4.e.c 95.e 19.c $20$ $5.605$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(-5\) \(50\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{2}q^{3}+(4\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(95, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)