Properties

Label 3024.1.o
Level $3024$
Weight $1$
Character orbit 3024.o
Rep. character $\chi_{3024}(3023,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3024.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3024, [\chi])\).

Total New Old
Modular forms 86 8 78
Cusp forms 50 8 42
Eisenstein series 36 0 36

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + O(q^{10}) \) \( 8q + 4q^{25} + 8q^{37} + 2q^{49} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3024.1.o.a \(2\) \(1.509\) \(\Q(\sqrt{3}) \) \(D_{6}\) \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{5}-q^{7}-\beta q^{11}+q^{19}+\beta q^{23}+\cdots\)
3024.1.o.b \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}-q^{19}+\cdots\)
3024.1.o.c \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{19}+\cdots\)
3024.1.o.d \(2\) \(1.509\) \(\Q(\sqrt{3}) \) \(D_{6}\) \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{5}+q^{7}+\beta q^{11}-q^{19}-\beta q^{23}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)