Properties

Label 304.2.k
Level $304$
Weight $2$
Character orbit 304.k
Rep. character $\chi_{304}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

Total New Old
Modular forms 84 72 12
Cusp forms 76 72 4
Eisenstein series 8 0 8

Trace form

\( 72q - 4q^{4} - 12q^{6} + O(q^{10}) \) \( 72q - 4q^{4} - 12q^{6} - 8q^{11} + 4q^{12} + 12q^{14} + 20q^{16} + 16q^{20} - 4q^{22} + 4q^{24} - 16q^{26} + 24q^{27} - 24q^{28} - 16q^{29} + 24q^{30} - 20q^{32} - 32q^{34} + 52q^{36} - 16q^{37} - 8q^{40} - 20q^{42} - 24q^{43} - 12q^{44} - 40q^{47} + 20q^{48} - 72q^{49} + 24q^{50} - 40q^{51} - 28q^{52} + 16q^{53} - 56q^{54} + 28q^{56} + 48q^{58} + 8q^{59} - 96q^{60} - 12q^{62} + 40q^{63} - 64q^{64} - 16q^{65} - 44q^{66} + 40q^{67} - 40q^{68} + 20q^{70} + 76q^{72} + 72q^{74} + 32q^{75} + 16q^{77} + 60q^{78} - 88q^{80} - 72q^{81} + 4q^{82} + 40q^{83} + 84q^{84} - 36q^{86} - 40q^{88} - 56q^{90} + 16q^{91} + 72q^{92} - 48q^{93} - 24q^{94} + 32q^{95} + 56q^{96} - 80q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.2.k.a \(4\) \(2.427\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(-8\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
304.2.k.b \(68\) \(2.427\) None \(0\) \(4\) \(8\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)