Properties

Label 1400.2.x
Level $1400$
Weight $2$
Character orbit 1400.x
Rep. character $\chi_{1400}(657,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $3$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(480\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

Total New Old
Modular forms 528 72 456
Cusp forms 432 72 360
Eisenstein series 96 0 96

Trace form

\( 72q - 4q^{7} + O(q^{10}) \) \( 72q - 4q^{7} - 16q^{11} - 32q^{21} + 32q^{23} + 8q^{37} - 16q^{43} + 48q^{51} + 16q^{53} - 20q^{63} + 32q^{67} + 64q^{71} + 40q^{77} + 24q^{81} + 8q^{91} - 72q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1400.2.x.a \(16\) \(11.179\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}-\beta _{1}q^{7}-\beta _{4}q^{9}+(-1-\beta _{9}+\cdots)q^{11}+\cdots\)
1400.2.x.b \(24\) \(11.179\) None \(0\) \(0\) \(0\) \(-4\)
1400.2.x.c \(32\) \(11.179\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)