Properties

Label 198.2.n
Level $198$
Weight $2$
Character orbit 198.n
Rep. character $\chi_{198}(29,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $96$
Newform subspaces $2$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 198.n (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(2\)
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

\( 96q - 4q^{3} + 12q^{4} - 6q^{5} + 5q^{6} - 20q^{9} + O(q^{10}) \) \( 96q - 4q^{3} + 12q^{4} - 6q^{5} + 5q^{6} - 20q^{9} - 15q^{11} + 12q^{12} + 6q^{15} + 12q^{16} - 10q^{18} + 30q^{19} + 6q^{20} + 3q^{22} + 36q^{23} - 5q^{24} - 18q^{25} - 34q^{27} - 90q^{29} - 30q^{30} + 6q^{31} - 22q^{33} + 6q^{34} - 15q^{36} - 12q^{37} - 60q^{38} - 70q^{39} - 44q^{42} - 20q^{45} + 6q^{47} + 2q^{48} - 12q^{49} + 15q^{51} + 12q^{55} - 50q^{57} + 18q^{58} - 117q^{59} - 8q^{60} - 10q^{63} - 24q^{64} + 40q^{66} - 30q^{67} - 64q^{69} + 12q^{70} + 20q^{72} + 63q^{75} - 54q^{77} - 80q^{78} + 96q^{81} - 18q^{82} + 90q^{83} + 60q^{84} + 39q^{86} + 3q^{88} + 140q^{90} - 72q^{91} + 54q^{92} + 110q^{93} + 240q^{95} - 15q^{97} + 2q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
198.2.n.a \(48\) \(1.581\) None \(-6\) \(-2\) \(-3\) \(0\)
198.2.n.b \(48\) \(1.581\) None \(6\) \(-2\) \(-3\) \(0\)

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

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