Properties

Label 345.2.i
Level $345$
Weight $2$
Character orbit 345.i
Rep. character $\chi_{345}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $3$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

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

Trace form

\( 88q - 8q^{7} + O(q^{10}) \) \( 88q - 8q^{7} - 8q^{10} - 16q^{13} + 12q^{15} - 88q^{16} - 28q^{18} + 8q^{21} + 24q^{22} + 12q^{27} - 24q^{28} + 16q^{30} - 16q^{31} + 4q^{33} - 48q^{37} + 64q^{40} - 32q^{42} - 32q^{43} - 24q^{45} + 28q^{48} - 24q^{51} + 32q^{52} - 24q^{55} - 40q^{57} + 8q^{58} + 20q^{60} + 16q^{61} + 68q^{63} + 72q^{66} + 16q^{67} - 104q^{70} + 36q^{72} + 24q^{73} - 36q^{75} + 16q^{76} - 100q^{78} - 8q^{81} + 16q^{82} + 32q^{85} - 40q^{87} + 120q^{88} - 4q^{90} - 96q^{91} - 56q^{93} - 80q^{96} - 8q^{97} + O(q^{100}) \)

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.i.a \(4\) \(2.755\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(-8\) \(q+(-1+\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\cdots\)
345.2.i.b \(4\) \(2.755\) \(\Q(\zeta_{8})\) None \(4\) \(0\) \(0\) \(-8\) \(q+(1+\zeta_{8}^{2})q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
345.2.i.c \(80\) \(2.755\) None \(0\) \(4\) \(0\) \(8\)