Properties

Label 345.2.b
Level $345$
Weight $2$
Character orbit 345.b
Rep. character $\chi_{345}(139,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(345, [\chi])\).

Total New Old
Modular forms 52 24 28
Cusp forms 44 24 20
Eisenstein series 8 0 8

Trace form

\( 24q - 28q^{4} + 4q^{5} + 4q^{6} - 24q^{9} + O(q^{10}) \) \( 24q - 28q^{4} + 4q^{5} + 4q^{6} - 24q^{9} - 8q^{14} - 4q^{15} + 36q^{16} + 8q^{19} + 4q^{20} - 8q^{21} - 12q^{24} - 32q^{26} + 12q^{29} - 8q^{30} + 20q^{31} + 32q^{34} - 36q^{35} + 28q^{36} - 8q^{39} + 24q^{40} + 28q^{41} - 40q^{44} - 4q^{45} + 8q^{46} - 52q^{49} + 48q^{50} - 4q^{54} + 12q^{59} + 36q^{60} - 100q^{64} + 16q^{65} - 8q^{66} - 8q^{69} + 64q^{70} - 4q^{71} - 88q^{74} + 8q^{75} - 32q^{76} + 40q^{79} + 76q^{80} + 24q^{81} + 56q^{84} + 12q^{85} - 48q^{86} - 48q^{89} - 48q^{91} - 80q^{94} + 8q^{95} + 28q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(345, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
345.2.b.a \(2\) \(2.755\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(1+2i)q^{5}-q^{6}+\cdots\)
345.2.b.b \(2\) \(2.755\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
345.2.b.c \(6\) \(2.755\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
345.2.b.d \(14\) \(2.755\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(-2-\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(345, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)