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Properties

Label 198.2.m
Level $198$
Weight $2$
Character orbit 198.m
Rep. character $\chi_{198}(25,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $96$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 198.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(198, [\chi])\).

Total New Old
Modular forms 320 96 224
Cusp forms 256 96 160
Eisenstein series 64 0 64

Trace form

\( 96 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{8} + 28 q^{9} + O(q^{10}) \) \( 96 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{8} + 28 q^{9} - 5 q^{11} - 12 q^{12} - 14 q^{15} + 12 q^{16} - 12 q^{17} + 14 q^{18} - 18 q^{19} - 2 q^{20} + 4 q^{21} - 3 q^{22} - 28 q^{23} - 3 q^{24} + 6 q^{25} - 24 q^{26} - 50 q^{27} + 46 q^{29} - 18 q^{30} - 6 q^{31} - 8 q^{32} - 42 q^{33} - 6 q^{34} - 76 q^{35} + q^{36} + 12 q^{37} + 16 q^{38} - 26 q^{39} - 22 q^{41} - 44 q^{42} - 6 q^{43} - 4 q^{45} + 22 q^{47} - 2 q^{48} + 12 q^{49} - 2 q^{50} - 59 q^{51} - 100 q^{53} - 10 q^{54} - 12 q^{55} + 16 q^{57} - 18 q^{58} - q^{59} + 12 q^{60} - 32 q^{62} - 2 q^{63} - 24 q^{64} - 84 q^{65} - 40 q^{66} + 18 q^{67} + 6 q^{68} + 44 q^{69} + 12 q^{70} - 12 q^{71} - 10 q^{72} + 12 q^{73} + 4 q^{74} - 105 q^{75} - 6 q^{76} + 26 q^{77} + 112 q^{78} - 12 q^{79} + 4 q^{80} - 48 q^{81} - 18 q^{82} + 4 q^{83} + 24 q^{84} - 24 q^{85} + 13 q^{86} + 144 q^{87} - 3 q^{88} + 232 q^{89} + 4 q^{90} - 72 q^{91} + 22 q^{92} + 70 q^{93} + 112 q^{95} - 4 q^{96} + 3 q^{97} + 144 q^{98} + 232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(198, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
198.2.m.a 198.m 99.m $40$ $1.581$ None \(-5\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{15}]$
198.2.m.b 198.m 99.m $56$ $1.581$ None \(7\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(198, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(198, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)