Properties

Label 336.2.s
Level 336
Weight 2
Character orbit s
Rep. character \(\chi_{336}(155,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 96
Newforms 4
Sturm bound 128
Trace bound 2

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 48 \)
Character field: \(\Q(i)\)
Newforms: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

Total New Old
Modular forms 136 96 40
Cusp forms 120 96 24
Eisenstein series 16 0 16

Trace form

\( 96q + 12q^{6} + O(q^{10}) \) \( 96q + 12q^{6} - 8q^{10} + 12q^{12} - 24q^{16} + 16q^{19} - 16q^{22} - 32q^{24} - 24q^{27} - 48q^{30} - 8q^{34} - 8q^{36} - 48q^{39} - 32q^{43} + 88q^{46} + 52q^{48} + 96q^{49} + 48q^{52} - 64q^{55} - 88q^{58} + 8q^{60} - 32q^{61} - 72q^{64} - 92q^{66} - 32q^{67} - 24q^{70} - 88q^{72} + 56q^{75} - 24q^{76} - 40q^{78} - 32q^{82} - 32q^{85} + 112q^{87} + 136q^{88} - 8q^{90} - 48q^{93} + 48q^{94} - 32q^{96} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
336.2.s.a \(4\) \(2.683\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(-4\) \(-4\) \(q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots\)
336.2.s.b \(4\) \(2.683\) \(\Q(\zeta_{8})\) None \(4\) \(0\) \(4\) \(-4\) \(q+(1+\zeta_{8})q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{4}+\cdots\)
336.2.s.c \(40\) \(2.683\) None \(0\) \(4\) \(0\) \(-40\)
336.2.s.d \(48\) \(2.683\) None \(0\) \(0\) \(0\) \(48\)

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)