Properties

Label 912.3.o
Level $912$
Weight $3$
Character orbit 912.o
Rep. character $\chi_{912}(721,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $5$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 332 40 292
Cusp forms 308 40 268
Eisenstein series 24 0 24

Trace form

\( 40q + 16q^{7} - 120q^{9} + O(q^{10}) \) \( 40q + 16q^{7} - 120q^{9} - 32q^{19} - 48q^{23} + 200q^{25} + 192q^{35} - 48q^{39} + 32q^{43} + 192q^{47} + 200q^{49} + 240q^{55} + 24q^{57} + 128q^{61} - 48q^{63} - 80q^{73} + 160q^{77} + 360q^{81} - 160q^{83} + 192q^{85} + 288q^{87} + 96q^{93} + 64q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
912.3.o.a \(2\) \(24.850\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(8\) \(20\) \(q-\zeta_{6}q^{3}+4q^{5}+10q^{7}-3q^{9}-10q^{11}+\cdots\)
912.3.o.b \(4\) \(24.850\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-10\) \(-34\) \(q-\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+(-8-\beta _{2}+\cdots)q^{7}+\cdots\)
912.3.o.c \(6\) \(24.850\) 6.0.219615408.1 None \(0\) \(0\) \(-2\) \(2\) \(q+\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-3q^{9}+(4+\cdots)q^{11}+\cdots\)
912.3.o.d \(8\) \(24.850\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(4\) \(12\) \(q+\beta _{2}q^{3}+(1+\beta _{1}-\beta _{4})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
912.3.o.e \(20\) \(24.850\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{7}q^{3}-\beta _{4}q^{5}+(1+\beta _{3})q^{7}-3q^{9}+\cdots\)

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

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