Properties

Label 700.2.t
Level $700$
Weight $2$
Character orbit 700.t
Rep. character $\chi_{700}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $136$
Newform subspaces $5$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

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

Total New Old
Modular forms 264 152 112
Cusp forms 216 136 80
Eisenstein series 48 16 32

Trace form

\( 136q + 2q^{4} + 64q^{9} + O(q^{10}) \) \( 136q + 2q^{4} + 64q^{9} + 18q^{14} - 10q^{16} + 12q^{21} - 12q^{24} + 6q^{26} + 32q^{29} + 60q^{36} + 4q^{44} + 4q^{46} - 102q^{54} - 38q^{56} - 12q^{61} - 88q^{64} - 96q^{66} - 62q^{74} - 108q^{81} - 94q^{84} + 56q^{86} + 132q^{89} - 66q^{94} + 18q^{96} + O(q^{100}) \)

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.t.a \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(0\) \(-8\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
700.2.t.b \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(2\) \(6\) \(0\) \(8\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
700.2.t.c \(32\) \(5.590\) None \(0\) \(0\) \(0\) \(0\)
700.2.t.d \(32\) \(5.590\) None \(0\) \(0\) \(0\) \(0\)
700.2.t.e \(64\) \(5.590\) None \(0\) \(0\) \(0\) \(0\)

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

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