Properties

Label 350.2.j
Level $350$
Weight $2$
Character orbit 350.j
Rep. character $\chi_{350}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $6$
Sturm bound $120$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(120\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).

Total New Old
Modular forms 144 24 120
Cusp forms 96 24 72
Eisenstein series 48 0 48

Trace form

\( 24q + 12q^{4} + 16q^{6} + 8q^{9} + O(q^{10}) \) \( 24q + 12q^{4} + 16q^{6} + 8q^{9} + 8q^{11} + 4q^{14} - 12q^{16} + 4q^{19} - 20q^{21} + 8q^{24} - 16q^{26} - 24q^{29} - 12q^{31} - 16q^{34} + 16q^{36} - 32q^{39} - 8q^{41} - 8q^{44} - 24q^{46} + 48q^{49} + 12q^{51} + 20q^{54} - 4q^{56} + 4q^{59} + 16q^{61} - 24q^{64} - 8q^{71} + 12q^{74} + 8q^{76} - 28q^{79} + 28q^{81} - 4q^{84} + 16q^{86} + 16q^{89} - 4q^{91} - 4q^{94} - 8q^{96} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
350.2.j.a \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
350.2.j.b \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.c \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots\)
350.2.j.d \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.e \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.f \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

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