Properties

Label 196.3.b
Level $196$
Weight $3$
Character orbit 196.b
Rep. character $\chi_{196}(97,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 196.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(196, [\chi])\).

Total New Old
Modular forms 68 6 62
Cusp forms 44 6 38
Eisenstein series 24 0 24

Trace form

\( 6 q + 8 q^{9} + O(q^{10}) \) \( 6 q + 8 q^{9} + 6 q^{11} - 66 q^{15} + 86 q^{23} - 64 q^{25} + 20 q^{29} - 66 q^{37} + 136 q^{39} + 60 q^{43} - 222 q^{51} - 90 q^{53} + 134 q^{57} + 144 q^{65} + 14 q^{67} - 28 q^{71} + 94 q^{79} + 54 q^{81} - 114 q^{85} - 294 q^{93} - 302 q^{95} - 188 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.3.b.a 196.b 7.b $2$ $5.341$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+6q^{9}+15q^{11}+\cdots\)
196.3.b.b 196.b 7.b $4$ $5.341$ 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(-1-\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)