Properties

Label 196.2.d
Level $196$
Weight $2$
Character orbit 196.d
Rep. character $\chi_{196}(195,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 36 24 12
Cusp forms 20 16 4
Eisenstein series 16 8 8

Trace form

\( 16q + 4q^{4} - 12q^{8} + 12q^{9} + O(q^{10}) \) \( 16q + 4q^{4} - 12q^{8} + 12q^{9} + 4q^{16} - 20q^{18} + 12q^{22} - 4q^{25} - 16q^{29} - 28q^{30} + 20q^{32} - 20q^{36} - 20q^{37} + 16q^{44} - 4q^{46} - 4q^{50} + 28q^{53} - 4q^{57} - 8q^{58} + 32q^{60} - 20q^{64} + 8q^{65} - 4q^{72} - 12q^{74} + 32q^{78} - 56q^{81} - 20q^{85} + 72q^{86} - 72q^{88} + 64q^{92} - 44q^{93} + O(q^{100}) \)

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.d.a \(4\) \(1.565\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots\)
196.2.d.b \(4\) \(1.565\) \(\Q(\zeta_{12})\) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\)
196.2.d.c \(8\) \(1.565\) 8.0.\(\cdots\).10 None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots\)

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

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