Properties

Label 1872.2.by
Level $1872$
Weight $2$
Character orbit 1872.by
Rep. character $\chi_{1872}(433,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $15$
Sturm bound $672$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.by (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 15 \)
Sturm bound: \(672\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 720 72 648
Cusp forms 624 68 556
Eisenstein series 96 4 92

Trace form

\( 68 q - 3 q^{7} + O(q^{10}) \) \( 68 q - 3 q^{7} - 3 q^{11} - q^{13} + 2 q^{17} + 3 q^{19} + 5 q^{23} - 62 q^{25} + 16 q^{35} - 6 q^{37} - 5 q^{43} + 27 q^{49} + 10 q^{53} + 24 q^{55} - 45 q^{59} - 4 q^{61} - 27 q^{65} - 27 q^{67} - 39 q^{71} + 26 q^{77} + 24 q^{79} + 15 q^{85} + 3 q^{89} + 13 q^{91} + 18 q^{95} - 3 q^{97} + O(q^{100}) \)

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.by.a 1872.by 13.e $2$ $14.948$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-9\) $\mathrm{U}(1)[D_{6}]$ \(q+(-6+3\zeta_{6})q^{7}+(-4+3\zeta_{6})q^{13}+\cdots\)
1872.2.by.b 1872.by 13.e $2$ $14.948$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+(2+\cdots)q^{11}+\cdots\)
1872.2.by.c 1872.by 13.e $2$ $14.948$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-3\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+\zeta_{6})q^{7}+(4-\zeta_{6})q^{13}+(-4+\cdots)q^{19}+\cdots\)
1872.2.by.d 1872.by 13.e $2$ $14.948$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{5}+(-1-3\zeta_{6})q^{13}+\cdots\)
1872.2.by.e 1872.by 13.e $2$ $14.948$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+(-3+\cdots)q^{13}+\cdots\)
1872.2.by.f 1872.by 13.e $2$ $14.948$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-4\zeta_{6})q^{5}+(2-\zeta_{6})q^{7}+(-2-2\zeta_{6})q^{11}+\cdots\)
1872.2.by.g 1872.by 13.e $4$ $14.948$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{12}^{2})q^{5}+(-2-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1872.2.by.h 1872.by 13.e $4$ $14.948$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1872.2.by.i 1872.by 13.e $4$ $14.948$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{5}+(-4+3\zeta_{12}^{2})q^{13}+(-\zeta_{12}+\cdots)q^{17}+\cdots\)
1872.2.by.j 1872.by 13.e $4$ $14.948$ \(\Q(\sqrt{-3}, \sqrt{-43})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
1872.2.by.k 1872.by 13.e $4$ $14.948$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{12}^{2})q^{5}+(1+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1872.2.by.l 1872.by 13.e $4$ $14.948$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{5}+(2+2\beta _{2})q^{7}+(2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
1872.2.by.m 1872.by 13.e $8$ $14.948$ 8.0.649638144.4 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{6})q^{5}+(-1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1872.2.by.n 1872.by 13.e $8$ $14.948$ 8.0.195105024.2 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{3}-\beta _{5}+\beta _{6})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1872.2.by.o 1872.by 13.e $16$ $14.948$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{12}q^{5}-\beta _{2}q^{7}+(-\beta _{5}+\beta _{8}-\beta _{12}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)