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Properties

Label 912.3.be
Level $912$
Weight $3$
Character orbit 912.be
Rep. character $\chi_{912}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $10$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(480\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 664 80 584
Cusp forms 616 80 536
Eisenstein series 48 0 48

Trace form

\( 80 q - 16 q^{7} + 120 q^{9} + O(q^{10}) \) \( 80 q - 16 q^{7} + 120 q^{9} - 16 q^{19} + 48 q^{23} - 200 q^{25} - 192 q^{35} + 48 q^{39} - 48 q^{41} + 16 q^{43} + 96 q^{47} + 640 q^{49} + 144 q^{51} - 48 q^{53} - 96 q^{55} - 24 q^{57} + 16 q^{61} - 24 q^{63} - 384 q^{67} - 144 q^{71} - 40 q^{73} - 160 q^{77} + 168 q^{79} - 360 q^{81} + 160 q^{83} + 96 q^{85} + 576 q^{87} - 288 q^{89} + 96 q^{91} - 96 q^{93} + 416 q^{95} - 144 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.3.be.a 912.be 19.d $2$ $24.850$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-6\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-6+6\zeta_{6})q^{5}+5q^{7}+\cdots\)
912.3.be.b 912.be 19.d $2$ $24.850$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(2\) \(-22\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-11q^{7}+\cdots\)
912.3.be.c 912.be 19.d $2$ $24.850$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(2\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+q^{7}+\cdots\)
912.3.be.d 912.be 19.d $6$ $24.850$ 6.0.6967728.1 None \(0\) \(-9\) \(-2\) \(-26\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2-\beta _{3})q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-4+\cdots)q^{7}+\cdots\)
912.3.be.e 912.be 19.d $6$ $24.850$ 6.0.954288.1 None \(0\) \(9\) \(4\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{2})q^{3}+(\beta _{1}+2\beta _{2}-\beta _{4}+\beta _{5})q^{5}+\cdots\)
912.3.be.f 912.be 19.d $6$ $24.850$ 6.0.92607408.1 None \(0\) \(9\) \(4\) \(22\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{3})q^{3}+(2-\beta _{1}-\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots\)
912.3.be.g 912.be 19.d $8$ $24.850$ 8.0.\(\cdots\).10 None \(0\) \(-12\) \(4\) \(24\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{4})q^{5}+\cdots\)
912.3.be.h 912.be 19.d $8$ $24.850$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(12\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{4})q^{3}+(2\beta _{4}-\beta _{5}-\beta _{7})q^{5}+\cdots\)
912.3.be.i 912.be 19.d $20$ $24.850$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-30\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3})q^{3}+(-\beta _{2}-\beta _{13})q^{5}+\cdots\)
912.3.be.j 912.be 19.d $20$ $24.850$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(30\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{3})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{15}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)