Properties

Label 196.2.f
Level $196$
Weight $2$
Character orbit 196.f
Rep. character $\chi_{196}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $4$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(196, [\chi])\).

Total New Old
Modular forms 72 48 24
Cusp forms 40 32 8
Eisenstein series 32 16 16

Trace form

\( 32q + 3q^{2} - q^{4} + 6q^{5} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 32q + 3q^{2} - q^{4} + 6q^{5} - 6q^{8} - 6q^{9} - 6q^{10} - 12q^{12} - 13q^{16} + 6q^{17} + 17q^{18} + 12q^{24} - 2q^{25} + 12q^{26} - 56q^{29} + 34q^{30} - 17q^{32} - 6q^{33} - 22q^{36} + 14q^{37} - 18q^{38} - 12q^{40} - 34q^{44} - 8q^{46} - 26q^{50} - 10q^{53} + 18q^{54} + 28q^{57} + 14q^{58} - 20q^{60} + 18q^{61} - 22q^{64} - 20q^{65} + 6q^{66} + 19q^{72} - 30q^{73} + 24q^{74} + 40q^{78} + 24q^{80} + 20q^{81} - 12q^{82} - 52q^{85} - 54q^{86} + 54q^{88} - 54q^{89} + 92q^{92} + 38q^{93} + 30q^{94} + 24q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
196.2.f.a \(4\) \(1.565\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(6\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
196.2.f.b \(4\) \(1.565\) \(\Q(\sqrt{-3}, \sqrt{-7})\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
196.2.f.c \(8\) \(1.565\) 8.0.339738624.1 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}-\beta _{3}q^{5}+\cdots\)
196.2.f.d \(16\) \(1.565\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q+(-\beta _{6}-\beta _{11})q^{2}+(2\beta _{1}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)