Properties

Label 3724.1.e
Level $3724$
Weight $1$
Character orbit 3724.e
Rep. character $\chi_{3724}(1177,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $560$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3724.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(560\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3724, [\chi])\).

Total New Old
Modular forms 38 5 33
Cusp forms 14 5 9
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5q + q^{5} + 5q^{9} + O(q^{10}) \) \( 5q + q^{5} + 5q^{9} + q^{11} + q^{17} - q^{19} - 2q^{23} + 6q^{25} + q^{43} + q^{45} + q^{47} - q^{55} + q^{61} + q^{73} + 5q^{81} - 2q^{83} - q^{85} + q^{95} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3724, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3724.1.e.a \(1\) \(1.859\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+\cdots\)
3724.1.e.b \(1\) \(1.859\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}+q^{9}+2q^{11}-q^{17}+q^{19}+\cdots\)
3724.1.e.c \(1\) \(1.859\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(0\) \(q+q^{5}+q^{9}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots\)
3724.1.e.d \(1\) \(1.859\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(0\) \(q+q^{5}+q^{9}+2q^{11}+q^{17}-q^{19}+\cdots\)
3724.1.e.e \(1\) \(1.859\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3724, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3724, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 3}\)