Properties

Label 912.2.bo
Level $912$
Weight $2$
Character orbit 912.bo
Rep. character $\chi_{912}(289,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $120$
Newform subspaces $12$
Sturm bound $320$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 12 \)
Sturm bound: \(320\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

Total New Old
Modular forms 1032 120 912
Cusp forms 888 120 768
Eisenstein series 144 0 144

Trace form

\( 120q + O(q^{10}) \) \( 120q - 6q^{19} - 6q^{27} + 36q^{31} + 24q^{41} - 6q^{43} + 36q^{47} - 60q^{49} + 12q^{51} + 24q^{53} - 36q^{55} + 24q^{61} + 12q^{63} - 24q^{65} + 66q^{67} + 24q^{69} + 72q^{71} - 12q^{73} + 84q^{75} + 84q^{79} + 72q^{85} + 36q^{87} - 24q^{89} + 12q^{91} + 60q^{95} + 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
912.2.bo.a \(6\) \(7.282\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-9\) \(-9\) \(q+\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}-\zeta_{18}^{3}-2\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.b \(6\) \(7.282\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-6\) \(-3\) \(q-\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.c \(6\) \(7.282\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(-3\) \(q+\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}+\zeta_{18}^{3}-2\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
912.2.bo.d \(6\) \(7.282\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(3\) \(q-\zeta_{18}q^{3}+(1-\zeta_{18}^{2}-\zeta_{18}^{3}-2\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
912.2.bo.e \(6\) \(7.282\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(6\) \(-3\) \(q+\zeta_{18}q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.f \(6\) \(7.282\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(9\) \(-3\) \(q-\zeta_{18}q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+2\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.g \(12\) \(7.282\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(9\) \(q+\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{5}+\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
912.2.bo.h \(12\) \(7.282\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{2}+\beta _{11})q^{3}-\beta _{1}q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.bo.i \(12\) \(7.282\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(3\) \(6\) \(q+\beta _{3}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.bo.j \(12\) \(7.282\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(6\) \(9\) \(q-\beta _{3}q^{3}+(1-2\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
912.2.bo.k \(18\) \(7.282\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{7}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
912.2.bo.l \(18\) \(7.282\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(3\) \(-6\) \(q-\beta _{9}q^{3}+(1+\beta _{5}-\beta _{6}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

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