Properties

Label 912.2.bn
Level $912$
Weight $2$
Character orbit 912.bn
Rep. character $\chi_{912}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $15$
Sturm bound $320$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 15 \)
Sturm bound: \(320\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 344 84 260
Cusp forms 296 76 220
Eisenstein series 48 8 40

Trace form

\( 76 q + 3 q^{3} + 4 q^{7} + q^{9} + O(q^{10}) \) \( 76 q + 3 q^{3} + 4 q^{7} + q^{9} - 6 q^{13} + 3 q^{15} + 12 q^{19} - 12 q^{21} + 28 q^{25} + 10 q^{39} - 12 q^{43} - 14 q^{45} + 52 q^{49} + 3 q^{51} + 4 q^{55} - 17 q^{57} + 14 q^{61} + 26 q^{63} + 36 q^{67} - 18 q^{73} + 48 q^{79} - 19 q^{81} - 22 q^{85} - 30 q^{87} + 90 q^{91} + 2 q^{93} - 42 q^{97} + 8 q^{99} + O(q^{100}) \)

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.bn.a \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-2\) \(q+(-1-\zeta_{6})q^{3}-q^{7}+3\zeta_{6}q^{9}+(2+\cdots)q^{13}+\cdots\)
912.2.bn.b \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(4\) \(q+(-1+2\zeta_{6})q^{3}+(2+2\zeta_{6})q^{5}+2q^{7}+\cdots\)
912.2.bn.c \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(-2\) \(q+(1+\zeta_{6})q^{3}+(-2-2\zeta_{6})q^{5}-q^{7}+\cdots\)
912.2.bn.d \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(4\) \(q+(2-\zeta_{6})q^{3}+(-2-2\zeta_{6})q^{5}+2q^{7}+\cdots\)
912.2.bn.e \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(10\) \(q+(1+\zeta_{6})q^{3}+5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots\)
912.2.bn.f \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(6\) \(-2\) \(q+(1+\zeta_{6})q^{3}+(2+2\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
912.2.bn.g \(4\) \(7.282\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+(-1-\beta _{3})q^{3}+\beta _{1}q^{5}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.bn.h \(4\) \(7.282\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-2\) \(0\) \(-8\) \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\beta _{1}q^{5}+(-2+\cdots)q^{7}+\cdots\)
912.2.bn.i \(4\) \(7.282\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-2\) \(3\) \(-2\) \(q+(-1+\beta _{1}-\beta _{3})q^{3}+(1-\beta _{1})q^{5}+\cdots\)
912.2.bn.j \(4\) \(7.282\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-3\) \(-2\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
912.2.bn.k \(4\) \(7.282\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(-9\) \(-2\) \(q+(\beta _{2}+\beta _{3})q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
912.2.bn.l \(4\) \(7.282\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(2\) \(9\) \(-2\) \(q+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.bn.m \(8\) \(7.282\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(16\) \(q+(\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{4})q^{3}-\zeta_{24}^{5}q^{5}+\cdots\)
912.2.bn.n \(16\) \(7.282\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-1\) \(3\) \(0\) \(q-\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
912.2.bn.o \(16\) \(7.282\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(1\) \(-3\) \(0\) \(q+\beta _{7}q^{3}+(\beta _{11}-\beta _{14})q^{5}+(-\beta _{5}+\beta _{13}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)