Properties

Label 700.2.r
Level $700$
Weight $2$
Character orbit 700.r
Rep. character $\chi_{700}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $4$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(11\)
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 24 252
Cusp forms 204 24 180
Eisenstein series 72 0 72

Trace form

\( 24q + 20q^{9} + O(q^{10}) \) \( 24q + 20q^{9} - 10q^{11} + 10q^{19} + 4q^{21} + 12q^{31} + 16q^{39} + 76q^{41} - 24q^{49} + 24q^{51} - 8q^{59} - 44q^{61} - 36q^{69} - 44q^{71} - 28q^{79} - 68q^{81} + 22q^{89} + 26q^{91} - 12q^{99} + O(q^{100}) \)

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.r.a \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
700.2.r.b \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
700.2.r.c \(4\) \(5.590\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots\)
700.2.r.d \(12\) \(5.590\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{4}-\beta _{10})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)

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

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