Properties

Label 3024.1.eg
Level $3024$
Weight $1$
Character orbit 3024.eg
Rep. character $\chi_{3024}(53,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $2$
Sturm bound $576$
Trace bound $10$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3024.eg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(10\)

Dimensions

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

Total New Old
Modular forms 80 16 64
Cusp forms 32 16 16
Eisenstein series 48 0 48

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 16 0

Trace form

\( 16q + O(q^{10}) \) \( 16q - 4q^{10} - 8q^{13} + 8q^{16} + 12q^{28} + 12q^{31} - 4q^{37} + 8q^{43} - 8q^{46} - 4q^{49} - 4q^{52} + 4q^{58} - 4q^{61} - 4q^{67} - 16q^{76} - 8q^{79} - 4q^{88} + 4q^{91} + 4q^{94} + 8q^{97} + O(q^{100}) \)

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.eg.a \(8\) \(1.509\) \(\Q(\zeta_{24})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
3024.1.eg.b \(8\) \(1.509\) \(\Q(\zeta_{24})\) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{10}q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)