Properties

Label 350.2.c
Level $350$
Weight $2$
Character orbit 350.c
Rep. character $\chi_{350}(99,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $120$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 72 8 64
Cusp forms 48 8 40
Eisenstein series 24 0 24

Trace form

\( 8q - 8q^{4} - 4q^{9} + O(q^{10}) \) \( 8q - 8q^{4} - 4q^{9} + 4q^{11} + 4q^{14} + 8q^{16} + 16q^{19} + 4q^{21} - 12q^{26} + 24q^{29} - 8q^{31} + 4q^{34} + 4q^{36} - 56q^{39} + 20q^{41} - 4q^{44} - 8q^{49} - 12q^{51} + 36q^{54} - 4q^{56} - 4q^{59} - 36q^{61} - 8q^{64} + 36q^{66} - 40q^{71} - 8q^{74} - 16q^{76} - 24q^{79} + 16q^{81} - 4q^{84} - 8q^{86} + 44q^{89} + 20q^{91} - 32q^{94} + 96q^{99} + O(q^{100}) \)

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.c.a \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{7}+\cdots\)
350.2.c.b \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
350.2.c.c \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
350.2.c.d \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)