Properties

Label 700.2.c
Level $700$
Weight $2$
Character orbit 700.c
Rep. character $\chi_{700}(699,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $11$
Sturm bound $240$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(240\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).

Total New Old
Modular forms 132 76 56
Cusp forms 108 68 40
Eisenstein series 24 8 16

Trace form

\( 68 q + 4 q^{4} - 52 q^{9} + O(q^{10}) \) \( 68 q + 4 q^{4} - 52 q^{9} + 12 q^{14} - 20 q^{16} - 24 q^{21} - 8 q^{29} - 12 q^{36} - 22 q^{44} + 50 q^{46} - 12 q^{49} + 50 q^{56} + 46 q^{64} - 82 q^{74} - 60 q^{81} - 56 q^{84} + 34 q^{86} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(700, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
700.2.c.a \(4\) \(5.590\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(-4\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+\cdots\)
700.2.c.b \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-8\) \(q+(-1-\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.c \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-8\) \(q+(-1-\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.d \(4\) \(5.590\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots\)
700.2.c.e \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(8\) \(q+(1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.f \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(8\) \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
700.2.c.g \(4\) \(5.590\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(4\) \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}-2\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
700.2.c.h \(8\) \(5.590\) 8.0.49787136.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{7}+\cdots\)
700.2.c.i \(8\) \(5.590\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{3}+\beta _{4})q^{3}+(\beta _{3}+\beta _{4}+\beta _{7})q^{4}+\cdots\)
700.2.c.j \(8\) \(5.590\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
700.2.c.k \(16\) \(5.590\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+(-\beta _{5}+\beta _{6}-\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)