Properties

Label 3744.2.g
Level $3744$
Weight $2$
Character orbit 3744.g
Rep. character $\chi_{3744}(1873,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $6$
Sturm bound $1344$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1344\)
Trace bound: \(1\)
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 60 644
Cusp forms 640 60 580
Eisenstein series 64 0 64

Trace form

\( 60 q + 4 q^{7} + O(q^{10}) \) \( 60 q + 4 q^{7} - 8 q^{23} - 60 q^{25} - 28 q^{31} + 8 q^{41} + 44 q^{47} + 60 q^{49} + 16 q^{55} - 20 q^{71} + 24 q^{79} - 16 q^{89} - 24 q^{95} - 16 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3744.2.g.a 3744.g 8.b $2$ $29.896$ \(\Q(\sqrt{-1}) \) None 104.2.b.a \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{5}-3 q^{7}-i q^{13}+7 q^{17}+\cdots\)
3744.2.g.b 3744.g 8.b $4$ $29.896$ \(\Q(\zeta_{12})\) None 104.2.b.b \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta_{2} q^{5}+(\beta_{3}+3)q^{7}+(\beta_{2}-3\beta_1)q^{11}+\cdots\)
3744.2.g.c 3744.g 8.b $6$ $29.896$ 6.0.399424.1 None 104.2.b.c \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+\beta _{1}q^{7}+(2\beta _{2}-\beta _{3}+\beta _{5})q^{11}+\cdots\)
3744.2.g.d 3744.g 8.b $8$ $29.896$ \(\Q(\zeta_{20})\) None 312.2.g.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta_{2}-\beta_1)q^{5}+(-\beta_{5}-1)q^{7}+\cdots\)
3744.2.g.e 3744.g 8.b $16$ $29.896$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 312.2.g.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{12}q^{5}-\beta _{5}q^{7}+\beta _{10}q^{11}-\beta _{6}q^{13}+\cdots\)
3744.2.g.f 3744.g 8.b $24$ $29.896$ None 936.2.g.f \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)