Properties

Label 1872.4.n
Level $1872$
Weight $4$
Character orbit 1872.n
Rep. character $\chi_{1872}(1871,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $5$
Sturm bound $1344$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1344\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 1032 84 948
Cusp forms 984 84 900
Eisenstein series 48 0 48

Trace form

\( 84 q + O(q^{10}) \) \( 84 q + 72 q^{13} + 2100 q^{25} + 4836 q^{49} + 1224 q^{61} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1872.4.n.a 1872.n 156.h $4$ $110.452$ \(\Q(\sqrt{-2}, \sqrt{13})\) \(\Q(\sqrt{-13}) \) \(0\) \(0\) \(0\) \(-76\) $\mathrm{U}(1)[D_{2}]$ \(q+(-19+5\beta _{1})q^{7}+(5\beta _{2}+5\beta _{3})q^{11}+\cdots\)
1872.4.n.b 1872.n 156.h $4$ $110.452$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{8}^{3}q^{5}+(-46-\zeta_{8})q^{13}+5\zeta_{8}^{2}q^{17}+\cdots\)
1872.4.n.c 1872.n 156.h $4$ $110.452$ \(\Q(\sqrt{-2}, \sqrt{13})\) \(\Q(\sqrt{-13}) \) \(0\) \(0\) \(0\) \(76\) $\mathrm{U}(1)[D_{2}]$ \(q+(19-5\beta _{1})q^{7}+(5\beta _{2}+5\beta _{3})q^{11}+\cdots\)
1872.4.n.d 1872.n 156.h $16$ $110.452$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+\beta _{10}q^{7}+\beta _{4}q^{11}+(11-\beta _{11}+\cdots)q^{13}+\cdots\)
1872.4.n.e 1872.n 156.h $56$ $110.452$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

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