Properties

Label 930.2.y
Level $930$
Weight $2$
Character orbit 930.y
Rep. character $\chi_{930}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $256$
Newform subspaces $2$
Sturm bound $384$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

Total New Old
Modular forms 800 256 544
Cusp forms 736 256 480
Eisenstein series 64 0 64

Trace form

\( 256q - 64q^{4} - 8q^{9} + O(q^{10}) \) \( 256q - 64q^{4} - 8q^{9} + 4q^{10} - 10q^{15} - 64q^{16} - 16q^{19} - 20q^{25} - 96q^{31} + 20q^{34} - 8q^{36} + 8q^{39} - 6q^{40} + 42q^{45} + 20q^{46} + 92q^{49} + 68q^{51} + 10q^{60} - 64q^{64} - 16q^{66} + 16q^{69} + 32q^{70} + 10q^{75} + 24q^{76} - 20q^{79} - 48q^{81} - 60q^{85} - 58q^{90} + 40q^{91} - 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
930.2.y.a \(128\) \(7.426\) None \(-32\) \(0\) \(2\) \(0\)
930.2.y.b \(128\) \(7.426\) None \(32\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)