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Properties

Label 198.6.l
Level $198$
Weight $6$
Character orbit 198.l
Rep. character $\chi_{198}(17,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $80$
Newform subspaces $2$
Sturm bound $216$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 198.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(198, [\chi])\).

Total New Old
Modular forms 752 80 672
Cusp forms 688 80 608
Eisenstein series 64 0 64

Trace form

\( 80 q - 320 q^{4} + O(q^{10}) \) \( 80 q - 320 q^{4} - 5120 q^{16} - 3312 q^{22} + 23148 q^{25} + 6080 q^{28} - 10604 q^{31} - 27968 q^{34} - 8688 q^{37} + 39680 q^{40} - 104800 q^{46} - 81396 q^{49} + 83840 q^{52} + 316792 q^{55} + 85264 q^{58} - 269560 q^{61} - 81920 q^{64} - 73712 q^{67} + 158800 q^{70} + 200060 q^{73} + 71800 q^{79} - 180192 q^{82} + 541200 q^{85} - 52992 q^{88} + 813312 q^{91} - 183200 q^{94} - 728328 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(198, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
198.6.l.a 198.l 33.f $40$ $31.756$ None 198.6.l.a \(-40\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
198.6.l.b 198.l 33.f $40$ $31.756$ None 198.6.l.a \(40\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{6}^{\mathrm{old}}(198, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(198, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)