Properties

Label 240.2.y
Level $240$
Weight $2$
Character orbit 240.y
Rep. character $\chi_{240}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $6$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

Total New Old
Modular forms 104 48 56
Cusp forms 88 48 40
Eisenstein series 16 0 16

Trace form

\( 48q - 4q^{4} + 12q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - 4q^{4} + 12q^{8} + 48q^{9} - 8q^{12} + 4q^{16} + 8q^{19} + 12q^{20} - 28q^{22} - 28q^{28} - 24q^{30} - 20q^{32} - 20q^{34} - 24q^{35} - 4q^{36} - 16q^{38} - 68q^{40} - 20q^{42} + 48q^{44} - 4q^{46} - 48q^{47} - 16q^{48} + 8q^{50} - 8q^{51} + 8q^{52} - 48q^{56} - 68q^{58} - 32q^{59} - 16q^{61} + 16q^{62} - 4q^{64} - 24q^{66} + 72q^{68} + 16q^{69} + 76q^{70} - 64q^{71} + 12q^{72} + 16q^{73} + 32q^{74} + 16q^{75} + 28q^{76} + 24q^{78} + 12q^{80} + 48q^{81} - 80q^{83} - 24q^{84} + 48q^{86} + 28q^{88} - 32q^{91} + 96q^{92} + 28q^{94} - 80q^{95} + 112q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
240.2.y.a \(2\) \(1.916\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
240.2.y.b \(2\) \(1.916\) \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(-2\) \(6\) \(q+(-1-i)q^{2}+q^{3}+2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
240.2.y.c \(2\) \(1.916\) \(\Q(\sqrt{-1}) \) None \(2\) \(-2\) \(2\) \(6\) \(q+(1+i)q^{2}-q^{3}+2iq^{4}+(1-2i)q^{5}+\cdots\)
240.2.y.d \(6\) \(1.916\) 6.0.399424.1 None \(0\) \(6\) \(6\) \(-2\) \(q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
240.2.y.e \(16\) \(1.916\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(2\) \(16\) \(-4\) \(-4\) \(q+\beta _{7}q^{2}+q^{3}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
240.2.y.f \(20\) \(1.916\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-20\) \(0\) \(-4\) \(q+\beta _{13}q^{2}-q^{3}-\beta _{3}q^{4}+\beta _{7}q^{5}-\beta _{13}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)