Properties

Label 198.2.a
Level $198$
Weight $2$
Character orbit 198.a
Rep. character $\chi_{198}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $72$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 198.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(198))\).

Total New Old
Modular forms 44 5 39
Cusp forms 29 5 24
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5 q - q^{2} + 5 q^{4} + 2 q^{5} - q^{8} + O(q^{10}) \) \( 5 q - q^{2} + 5 q^{4} + 2 q^{5} - q^{8} - 2 q^{10} + q^{11} - 2 q^{13} + 8 q^{14} + 5 q^{16} + 6 q^{17} + 4 q^{19} + 2 q^{20} - q^{22} - 4 q^{23} - 5 q^{25} - 2 q^{26} - 22 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 2 q^{37} - 8 q^{38} - 2 q^{40} - 2 q^{41} - 4 q^{43} + q^{44} - 8 q^{46} + 20 q^{47} - 3 q^{49} - 15 q^{50} - 2 q^{52} - 6 q^{53} - 6 q^{55} + 8 q^{56} - 2 q^{58} - 12 q^{59} - 34 q^{61} + 16 q^{62} + 5 q^{64} + 28 q^{65} + 4 q^{67} + 6 q^{68} + 4 q^{71} + 18 q^{73} - 14 q^{74} + 4 q^{76} + 24 q^{79} + 2 q^{80} + 2 q^{82} + 4 q^{83} + 12 q^{85} - q^{88} - 14 q^{89} + 16 q^{91} - 4 q^{92} + 16 q^{94} - 8 q^{95} + 2 q^{97} - 9 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(198))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
198.2.a.a 198.a 1.a $1$ $1.581$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}+2q^{10}+\cdots\)
198.2.a.b 198.a 1.a $1$ $1.581$ \(\Q\) None \(-1\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
198.2.a.c 198.a 1.a $1$ $1.581$ \(\Q\) None \(-1\) \(0\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-2q^{7}-q^{8}-4q^{10}+\cdots\)
198.2.a.d 198.a 1.a $1$ $1.581$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{11}+2q^{13}+\cdots\)
198.2.a.e 198.a 1.a $1$ $1.581$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}+q^{11}-4q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(198))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(198)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)