Properties

Label 99.2.m
Level $99$
Weight $2$
Character orbit 99.m
Rep. character $\chi_{99}(4,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $80$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).

Total New Old
Modular forms 112 112 0
Cusp forms 80 80 0
Eisenstein series 32 32 0

Trace form

\( 80 q - 5 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} - 7 q^{6} - 3 q^{7} - 8 q^{8} - 25 q^{9} + O(q^{10}) \) \( 80 q - 5 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} - 7 q^{6} - 3 q^{7} - 8 q^{8} - 25 q^{9} - 40 q^{10} - q^{11} + 2 q^{12} - 3 q^{13} - 11 q^{14} - 8 q^{15} + 5 q^{16} - 8 q^{17} - 24 q^{18} + 6 q^{19} - 21 q^{20} - 16 q^{21} - 5 q^{22} + 6 q^{23} - 3 q^{24} + 2 q^{25} - 28 q^{26} + 27 q^{27} - 36 q^{28} - 32 q^{29} + 12 q^{30} + 48 q^{32} + 28 q^{33} + 2 q^{34} + 30 q^{35} + 39 q^{36} - 18 q^{37} - 5 q^{38} - 35 q^{39} - 13 q^{40} + 13 q^{41} + 49 q^{42} - 2 q^{43} - 10 q^{44} + 16 q^{45} - 11 q^{47} - 50 q^{48} - 5 q^{49} - 24 q^{50} + 69 q^{51} - 15 q^{52} + 32 q^{53} + 88 q^{54} - 14 q^{55} + 102 q^{56} - 18 q^{57} + 7 q^{58} - 13 q^{59} - 63 q^{60} - 3 q^{61} + 190 q^{62} - 7 q^{63} - 8 q^{64} + 52 q^{65} + 105 q^{66} - 14 q^{67} - 32 q^{68} + 24 q^{69} - 52 q^{70} - 6 q^{71} + 41 q^{72} - 48 q^{73} + 81 q^{74} + 28 q^{75} + 10 q^{76} - 37 q^{77} - 40 q^{78} - 3 q^{79} - 4 q^{80} + 23 q^{81} - 2 q^{82} - 10 q^{83} + 3 q^{84} + 19 q^{85} - 56 q^{86} - 120 q^{87} + 55 q^{88} - 128 q^{89} - 22 q^{90} - 4 q^{91} + 29 q^{92} - 44 q^{93} - 35 q^{94} - 81 q^{95} - 97 q^{96} - 27 q^{97} - 256 q^{98} - 185 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(99, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.2.m.a 99.m 99.m $8$ $0.791$ \(\Q(\zeta_{15})\) None \(-4\) \(3\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{15}]$ \(q+(1-2\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
99.2.m.b 99.m 99.m $72$ $0.791$ None \(-1\) \(-12\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{15}]$