Properties

Label 684.2.c
Level $684$
Weight $2$
Character orbit 684.c
Rep. character $\chi_{684}(647,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).

Total New Old
Modular forms 128 36 92
Cusp forms 112 36 76
Eisenstein series 16 0 16

Trace form

\( 36q + O(q^{10}) \) \( 36q - 16q^{10} - 8q^{16} - 52q^{25} + 56q^{34} + 8q^{37} + 24q^{40} + 32q^{46} - 20q^{49} - 40q^{58} - 8q^{61} + 24q^{64} - 72q^{70} + 16q^{73} - 72q^{82} - 8q^{85} - 40q^{88} + 88q^{94} - 80q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
684.2.c.a \(4\) \(5.462\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+4\zeta_{8}q^{7}+\cdots\)
684.2.c.b \(32\) \(5.462\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)