Properties

Label 1344.2.s
Level 1344
Weight 2
Character orbit s
Rep. character \(\chi_{1344}(239,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 96
Newforms 4
Sturm bound 512
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1344.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 48 \)
Character field: \(\Q(i)\)
Newforms: \( 4 \)
Sturm bound: \(512\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

Total New Old
Modular forms 544 96 448
Cusp forms 480 96 384
Eisenstein series 64 0 64

Trace form

\( 96q + O(q^{10}) \) \( 96q - 16q^{19} + 24q^{27} + 48q^{39} + 32q^{43} + 96q^{49} + 64q^{55} - 32q^{61} + 32q^{67} - 56q^{75} - 32q^{85} - 112q^{87} - 48q^{93} - 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.2.s.a \(4\) \(10.732\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(4\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1344.2.s.b \(4\) \(10.732\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(-4\) \(4\) \(q+(1-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots\)
1344.2.s.c \(40\) \(10.732\) None \(0\) \(-4\) \(0\) \(40\)
1344.2.s.d \(48\) \(10.732\) None \(0\) \(0\) \(0\) \(-48\)

Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)