Properties

Label 1694.2.c
Level $1694$
Weight $2$
Character orbit 1694.c
Rep. character $\chi_{1694}(1693,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $3$
Sturm bound $528$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1694.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(528\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1694, [\chi])\).

Total New Old
Modular forms 288 72 216
Cusp forms 240 72 168
Eisenstein series 48 0 48

Trace form

\( 72q - 72q^{4} - 64q^{9} + O(q^{10}) \) \( 72q - 72q^{4} - 64q^{9} - 8q^{14} + 16q^{15} + 72q^{16} - 32q^{23} - 80q^{25} + 64q^{36} + 28q^{42} - 48q^{49} + 64q^{53} + 8q^{56} + 16q^{58} - 16q^{60} - 72q^{64} + 32q^{67} - 16q^{70} - 16q^{71} - 48q^{78} + 8q^{81} - 8q^{86} - 40q^{91} + 32q^{92} - 160q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1694.2.c.a \(8\) \(13.527\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}-q^{4}+\zeta_{16}^{2}q^{5}+\cdots\)
1694.2.c.b \(32\) \(13.527\) None \(0\) \(0\) \(0\) \(0\)
1694.2.c.c \(32\) \(13.527\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)