Properties

Label 3744.1.bd
Level $3744$
Weight $1$
Character orbit 3744.bd
Rep. character $\chi_{3744}(577,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $5$
Sturm bound $672$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3744.bd (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(672\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3744, [\chi])\).

Total New Old
Modular forms 96 10 86
Cusp forms 32 10 22
Eisenstein series 64 0 64

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10q - 2q^{5} + O(q^{10}) \) \( 10q - 2q^{5} - 4q^{13} + 2q^{37} + 2q^{41} + 4q^{53} - 12q^{61} + 2q^{65} + 2q^{73} + 4q^{85} + 2q^{89} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3744.1.bd.a \(2\) \(1.868\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-iq^{13}+iq^{25}-q^{29}+\cdots\)
3744.1.bd.b \(2\) \(1.868\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+iq^{13}+iq^{17}+iq^{25}+\cdots\)
3744.1.bd.c \(2\) \(1.868\) \(\Q(\sqrt{-1}) \) \(D_{4}\) None \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-1+i)q^{11}-q^{13}+iq^{23}-iq^{25}+\cdots\)
3744.1.bd.d \(2\) \(1.868\) \(\Q(\sqrt{-1}) \) \(D_{4}\) None \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(1-i)q^{11}-q^{13}-iq^{23}-iq^{25}+\cdots\)
3744.1.bd.e \(2\) \(1.868\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-iq^{13}+iq^{25}+q^{29}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1872, [\chi])\)\(^{\oplus 2}\)