Properties

Label 700.2.i
Level $700$
Weight $2$
Character orbit 700.i
Rep. character $\chi_{700}(401,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $26$
Newform subspaces $6$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

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

Total New Old
Modular forms 276 26 250
Cusp forms 204 26 178
Eisenstein series 72 0 72

Trace form

\( 26q - q^{3} - 2q^{7} - 18q^{9} + O(q^{10}) \) \( 26q - q^{3} - 2q^{7} - 18q^{9} - 3q^{11} + 4q^{13} - q^{17} - q^{19} - 9q^{21} - 3q^{23} + 38q^{27} + 4q^{29} + 11q^{31} + 9q^{33} + 15q^{37} + 18q^{39} - 4q^{43} - q^{47} + 14q^{49} - 3q^{51} + 19q^{53} - 14q^{57} + 7q^{59} - 15q^{61} - 22q^{63} - 17q^{67} - 78q^{69} - 36q^{71} + 3q^{73} - 7q^{77} + q^{79} - 21q^{81} - 28q^{83} - 12q^{87} + 31q^{89} + 50q^{91} - 11q^{93} + 60q^{97} + 48q^{99} + O(q^{100}) \)

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.i.a \(2\) \(5.590\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-1\) \(q+(-3+3\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}-6\zeta_{6}q^{9}+\cdots\)
700.2.i.b \(2\) \(5.590\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-5\) \(q+(1-\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
700.2.i.c \(2\) \(5.590\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(4\) \(q+(1-\zeta_{6})q^{3}+(3-2\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
700.2.i.d \(6\) \(5.590\) 6.0.1783323.2 None \(0\) \(-1\) \(0\) \(4\) \(q+(-\beta _{3}+\beta _{5})q^{3}+(1-\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
700.2.i.e \(6\) \(5.590\) 6.0.1783323.2 None \(0\) \(1\) \(0\) \(-4\) \(q+(\beta _{3}-\beta _{5})q^{3}+(-1+\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots\)
700.2.i.f \(8\) \(5.590\) 8.0.2702336256.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)