Properties

Label 3744.2.m
Level $3744$
Weight $2$
Character orbit 3744.m
Rep. character $\chi_{3744}(1585,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $9$
Sturm bound $1344$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(1344\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

Total New Old
Modular forms 704 72 632
Cusp forms 640 68 572
Eisenstein series 64 4 60

Trace form

\( 68 q + O(q^{10}) \) \( 68 q + 8 q^{23} + 52 q^{25} - 76 q^{49} + 24 q^{55} + 24 q^{65} - 16 q^{79} - 96 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3744.2.m.a $2$ $29.896$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-2q^{5}+4q^{11}+(-3+i)q^{13}+6q^{17}+\cdots\)
3744.2.m.b $2$ $29.896$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-3iq^{7}+2q^{11}+(-3-2i)q^{13}+\cdots\)
3744.2.m.c $2$ $29.896$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-3iq^{7}-2q^{11}+(3+2i)q^{13}+\cdots\)
3744.2.m.d $2$ $29.896$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2q^{5}-4q^{11}+(3-i)q^{13}+6q^{17}+\cdots\)
3744.2.m.e $4$ $29.896$ \(\Q(\sqrt{-2}, \sqrt{13})\) \(\Q(\sqrt{-78}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{13}-2\beta _{2}q^{19}-5q^{25}-\beta _{3}q^{29}+\cdots\)
3744.2.m.f $8$ $29.896$ 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(-\beta _{2}+\beta _{6})q^{11}-\beta _{1}q^{13}+\cdots\)
3744.2.m.g $8$ $29.896$ 8.0.4521217600.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{5}-\beta _{3}q^{7}+(\beta _{4}+\beta _{6})q^{11}+(-\beta _{6}+\cdots)q^{13}+\cdots\)
3744.2.m.h $16$ $29.896$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{5}+\beta _{5}q^{7}+(-\beta _{11}+\beta _{14}+\cdots)q^{11}+\cdots\)
3744.2.m.i $24$ $29.896$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)