Properties

Label 2916.3.c
Level $2916$
Weight $3$
Character orbit 2916.c
Rep. character $\chi_{2916}(1457,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $2$
Sturm bound $1458$
Trace bound $61$

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Defining parameters

Level: \( N \) \(=\) \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2916.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(1458\)
Trace bound: \(61\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2916, [\chi])\).

Total New Old
Modular forms 1026 72 954
Cusp forms 918 72 846
Eisenstein series 108 0 108

Trace form

\( 72 q + O(q^{10}) \) \( 72 q - 360 q^{25} + 504 q^{49} - 18 q^{61} + 90 q^{67} - 126 q^{73} - 216 q^{85} + 198 q^{91} + 432 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2916, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2916.3.c.a 2916.c 3.b $36$ $79.455$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2916.3.c.b 2916.c 3.b $36$ $79.455$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2916, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2916, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(486, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(729, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1458, [\chi])\)\(^{\oplus 2}\)