Properties

Label 198.4.a
Level $198$
Weight $4$
Character orbit 198.a
Rep. character $\chi_{198}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $10$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 198.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(198))\).

Total New Old
Modular forms 116 13 103
Cusp forms 100 13 87
Eisenstein series 16 0 16

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
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(8\)
Minus space\(-\)\(5\)

Trace form

\( 13 q - 2 q^{2} + 52 q^{4} - 12 q^{5} + 52 q^{7} - 8 q^{8} + O(q^{10}) \) \( 13 q - 2 q^{2} + 52 q^{4} - 12 q^{5} + 52 q^{7} - 8 q^{8} - 20 q^{10} - 11 q^{11} - 22 q^{13} + 32 q^{14} + 208 q^{16} - 66 q^{17} - 148 q^{19} - 48 q^{20} + 22 q^{22} + 426 q^{23} + 597 q^{25} - 100 q^{26} + 208 q^{28} + 198 q^{29} + 530 q^{31} - 32 q^{32} - 60 q^{34} + 780 q^{35} - 808 q^{37} + 32 q^{38} - 80 q^{40} - 78 q^{41} - 480 q^{43} - 44 q^{44} + 304 q^{46} - 828 q^{47} + 1485 q^{49} + 658 q^{50} - 88 q^{52} - 1326 q^{53} - 396 q^{55} + 128 q^{56} + 220 q^{58} - 210 q^{59} + 1914 q^{61} + 704 q^{62} + 832 q^{64} - 2244 q^{65} + 194 q^{67} - 264 q^{68} - 2160 q^{70} + 1086 q^{71} - 2810 q^{73} + 500 q^{74} - 592 q^{76} - 484 q^{77} - 2852 q^{79} - 192 q^{80} + 884 q^{82} - 864 q^{83} - 3120 q^{85} - 352 q^{86} + 88 q^{88} - 576 q^{89} + 2400 q^{91} + 1704 q^{92} - 2288 q^{94} + 5160 q^{95} - 1536 q^{97} - 2610 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(198))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
198.4.a.a 198.a 1.a $1$ $11.682$ \(\Q\) None 66.4.a.b \(-2\) \(0\) \(-10\) \(16\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-10q^{5}+2^{4}q^{7}-8q^{8}+\cdots\)
198.4.a.b 198.a 1.a $1$ $11.682$ \(\Q\) None 22.4.a.c \(-2\) \(0\) \(3\) \(-10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+3q^{5}-10q^{7}-8q^{8}+\cdots\)
198.4.a.c 198.a 1.a $1$ $11.682$ \(\Q\) None 198.4.a.c \(-2\) \(0\) \(8\) \(-22\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+8q^{5}-22q^{7}-8q^{8}+\cdots\)
198.4.a.d 198.a 1.a $1$ $11.682$ \(\Q\) None 22.4.a.b \(2\) \(0\) \(-14\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-14q^{5}-8q^{7}+8q^{8}+\cdots\)
198.4.a.e 198.a 1.a $1$ $11.682$ \(\Q\) None 198.4.a.c \(2\) \(0\) \(-8\) \(-22\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-8q^{5}-22q^{7}+8q^{8}+\cdots\)
198.4.a.f 198.a 1.a $1$ $11.682$ \(\Q\) None 66.4.a.a \(2\) \(0\) \(0\) \(14\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+14q^{7}+8q^{8}-11q^{11}+\cdots\)
198.4.a.g 198.a 1.a $1$ $11.682$ \(\Q\) None 22.4.a.a \(2\) \(0\) \(19\) \(14\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+19q^{5}+14q^{7}+8q^{8}+\cdots\)
198.4.a.h 198.a 1.a $2$ $11.682$ \(\Q(\sqrt{97}) \) None 66.4.a.c \(-4\) \(0\) \(-10\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-5-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
198.4.a.i 198.a 1.a $2$ $11.682$ \(\Q(\sqrt{70}) \) None 198.4.a.i \(-4\) \(0\) \(8\) \(36\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(4+\beta )q^{5}+(18+\beta )q^{7}+\cdots\)
198.4.a.j 198.a 1.a $2$ $11.682$ \(\Q(\sqrt{70}) \) None 198.4.a.i \(4\) \(0\) \(-8\) \(36\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-4+\beta )q^{5}+(18-\beta )q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(198))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(198)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)