Properties

Label 700.1.d
Level $700$
Weight $1$
Character orbit 700.d
Rep. character $\chi_{700}(601,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 700.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(700, [\chi])\).

Total New Old
Modular forms 26 2 24
Cusp forms 8 2 6
Eisenstein series 18 0 18

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + O(q^{10}) \) \( 2q - 2q^{11} - 2q^{21} + 2q^{29} - 2q^{39} - 2q^{49} + 2q^{51} + 4q^{71} + 2q^{79} - 2q^{81} - 2q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(700, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
700.1.d.a \(2\) \(0.349\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{11}-iq^{13}+iq^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)