Properties

Label 2016.3.m
Level $2016$
Weight $3$
Character orbit 2016.m
Rep. character $\chi_{2016}(127,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2016.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2016, [\chi])\).

Total New Old
Modular forms 800 60 740
Cusp forms 736 60 676
Eisenstein series 64 0 64

Trace form

\( 60q - 8q^{5} + O(q^{10}) \) \( 60q - 8q^{5} + 24q^{13} + 24q^{17} + 372q^{25} - 40q^{29} - 8q^{37} - 264q^{41} - 420q^{49} + 344q^{53} - 40q^{61} + 240q^{65} + 120q^{73} + 16q^{85} - 232q^{89} - 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2016.3.m.a \(4\) \(54.932\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(8\) \(0\) \(q+(2-\beta _{2})q^{5}+\beta _{3}q^{7}+(-2\beta _{1}+4\beta _{3})q^{11}+\cdots\)
2016.3.m.b \(8\) \(54.932\) 8.0.49787136.1 None \(0\) \(0\) \(-16\) \(0\) \(q+(-2+\beta _{6})q^{5}-\beta _{3}q^{7}+(\beta _{1}-2\beta _{3}+\cdots)q^{11}+\cdots\)
2016.3.m.c \(8\) \(54.932\) 8.0.1997017344.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{5}q^{7}+(-2\beta _{5}+\beta _{6}+\beta _{7})q^{11}+\cdots\)
2016.3.m.d \(12\) \(54.932\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-16\) \(0\) \(q+(-1+\beta _{1})q^{5}-\beta _{6}q^{7}+(-\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
2016.3.m.e \(12\) \(54.932\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(16\) \(0\) \(q+(1-\beta _{1})q^{5}-\beta _{6}q^{7}+(\beta _{3}-\beta _{6})q^{11}+\cdots\)
2016.3.m.f \(16\) \(54.932\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{4}q^{7}+(-\beta _{4}+\beta _{11})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)