Properties

Label 1872.2.d
Level $1872$
Weight $2$
Character orbit 1872.d
Rep. character $\chi_{1872}(287,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $672$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(672\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

Total New Old
Modular forms 360 24 336
Cusp forms 312 24 288
Eisenstein series 48 0 48

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 24 q^{25} - 72 q^{49} - 48 q^{73} - 96 q^{85} + 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1872.2.d.a 1872.d 12.b $4$ $14.948$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{3}q^{11}-q^{13}-\zeta_{8}^{2}q^{17}-\zeta_{8}q^{19}+\cdots\)
1872.2.d.b 1872.d 12.b $4$ $14.948$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{11}+q^{13}+\cdots\)
1872.2.d.c 1872.d 12.b $8$ $14.948$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{5}q^{5}+(-\zeta_{24}+\zeta_{24}^{3})q^{7}+\zeta_{24}^{2}q^{11}+\cdots\)
1872.2.d.d 1872.d 12.b $8$ $14.948$ 8.0.3317760000.8 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{5}q^{11}+q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)