Properties

Label 2520.1.h
Level $2520$
Weight $1$
Character orbit 2520.h
Rep. character $\chi_{2520}(1189,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $5$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2520.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2520, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 20 8 12
Eisenstein series 16 4 12

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

\( 8q + O(q^{10}) \) \( 8q - 4q^{14} + 8q^{16} + 4q^{25} + 4q^{50} + 4q^{56} - 4q^{65} - 4q^{70} - 8q^{79} + 4q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2520, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2520.1.h.a \(1\) \(1.258\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) \(\Q(\sqrt{105}) \) \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
2520.1.h.b \(1\) \(1.258\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) \(\Q(\sqrt{105}) \) \(-1\) \(0\) \(1\) \(1\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2520.1.h.c \(1\) \(1.258\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) \(\Q(\sqrt{105}) \) \(1\) \(0\) \(-1\) \(1\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
2520.1.h.d \(1\) \(1.258\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-70}) \) \(\Q(\sqrt{105}) \) \(1\) \(0\) \(1\) \(-1\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
2520.1.h.e \(4\) \(1.258\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)