Properties

Label 2646.2.d
Level $2646$
Weight $2$
Character orbit 2646.d
Rep. character $\chi_{2646}(2645,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $6$
Sturm bound $1008$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1008\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2646, [\chi])\).

Total New Old
Modular forms 552 52 500
Cusp forms 456 52 404
Eisenstein series 96 0 96

Trace form

\( 52 q - 52 q^{4} + O(q^{10}) \) \( 52 q - 52 q^{4} + 52 q^{16} - 4 q^{22} + 56 q^{25} - 44 q^{37} + 28 q^{43} + 32 q^{58} - 52 q^{64} + 36 q^{67} + 4 q^{79} - 72 q^{85} + 4 q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2646, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2646.2.d.a \(4\) \(21.128\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}q^{8}+\cdots\)
2646.2.d.b \(4\) \(21.128\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-q^{4}-2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{8}+\cdots\)
2646.2.d.c \(4\) \(21.128\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-q^{4}+\zeta_{12}q^{8}+3\zeta_{12}q^{11}+\cdots\)
2646.2.d.d \(8\) \(21.128\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{4}q^{5}-\zeta_{24}q^{8}+\cdots\)
2646.2.d.e \(16\) \(21.128\) \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}q^{2}-q^{4}+(\zeta_{48}^{9}+\zeta_{48}^{12})q^{5}+\cdots\)
2646.2.d.f \(16\) \(21.128\) \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}q^{2}-q^{4}+(-\zeta_{48}^{5}-\zeta_{48}^{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2646, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2646, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)