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Properties

Label 198.2.f
Level $198$
Weight $2$
Character orbit 198.f
Rep. character $\chi_{198}(37,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $20$
Newform subspaces $5$
Sturm bound $72$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 198.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 176 20 156
Cusp forms 112 20 92
Eisenstein series 64 0 64

Trace form

\( 20 q + q^{2} - 5 q^{4} - 2 q^{5} + 10 q^{7} + q^{8} + O(q^{10}) \) \( 20 q + q^{2} - 5 q^{4} - 2 q^{5} + 10 q^{7} + q^{8} + 12 q^{10} + 9 q^{11} + 12 q^{13} + 2 q^{14} - 5 q^{16} + 14 q^{17} + 11 q^{19} - 2 q^{20} + q^{22} + 4 q^{23} - 35 q^{25} - 18 q^{26} - 10 q^{28} + 2 q^{29} - 22 q^{31} - 4 q^{32} - 14 q^{34} - 40 q^{35} - 18 q^{37} - 22 q^{38} - 8 q^{40} - 18 q^{41} - 26 q^{43} + 4 q^{44} - 12 q^{46} + 20 q^{47} + 23 q^{49} + 35 q^{50} - 18 q^{52} + 16 q^{53} - 44 q^{55} - 8 q^{56} + 22 q^{58} + 7 q^{59} - 16 q^{61} + 14 q^{62} - 5 q^{64} - 8 q^{65} + 6 q^{67} + 14 q^{68} + 20 q^{70} - 4 q^{71} - 18 q^{73} + 34 q^{74} + 6 q^{76} - 14 q^{79} + 8 q^{80} + 33 q^{82} - 9 q^{83} + 18 q^{85} - 5 q^{86} + 11 q^{88} - 6 q^{89} + 84 q^{91} - 26 q^{92} + 4 q^{94} - 42 q^{95} + 53 q^{97} - 36 q^{98} + O(q^{100}) \)

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.f.a 198.f 11.c $4$ $1.581$ \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
198.2.f.b 198.f 11.c $4$ $1.581$ \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
198.2.f.c 198.f 11.c $4$ $1.581$ \(\Q(\zeta_{10})\) None \(1\) \(0\) \(-8\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
198.2.f.d 198.f 11.c $4$ $1.581$ \(\Q(\zeta_{10})\) None \(1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
198.2.f.e 198.f 11.c $4$ $1.581$ \(\Q(\zeta_{10})\) None \(1\) \(0\) \(6\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(198, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)