Properties

Label 2352.1.d
Level $2352$
Weight $1$
Character orbit 2352.d
Rep. character $\chi_{2352}(785,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2352.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(448\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2352, [\chi])\).

Total New Old
Modular forms 56 7 49
Cusp forms 8 2 6
Eisenstein series 48 5 43

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{9} + 2q^{25} - 2q^{37} + 2q^{39} + 2q^{43} - 2q^{57} + 2q^{67} + 2q^{79} + 2q^{81} - 2q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2352.1.d.a \(1\) \(1.174\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}-q^{13}+q^{19}+q^{25}-q^{27}+\cdots\)
2352.1.d.b \(1\) \(1.174\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}+q^{13}-q^{19}+q^{25}+q^{27}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)