Properties

Label 45.4.b
Level $45$
Weight $4$
Character orbit 45.b
Rep. character $\chi_{45}(19,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(45, [\chi])\).

Total New Old
Modular forms 22 8 14
Cusp forms 14 6 8
Eisenstein series 8 2 6

Trace form

\( 6 q - 12 q^{4} - 6 q^{5} + O(q^{10}) \) \( 6 q - 12 q^{4} - 6 q^{5} - 36 q^{10} + 84 q^{11} - 228 q^{14} - 12 q^{16} + 216 q^{19} + 396 q^{20} + 6 q^{25} + 12 q^{26} - 636 q^{29} - 360 q^{31} - 96 q^{34} + 300 q^{35} - 132 q^{40} + 816 q^{41} - 1116 q^{44} + 624 q^{46} + 546 q^{49} + 696 q^{50} - 864 q^{55} - 60 q^{56} - 372 q^{59} - 36 q^{61} - 108 q^{64} - 948 q^{65} + 1080 q^{70} + 72 q^{71} + 3132 q^{74} - 1464 q^{76} - 1368 q^{79} - 444 q^{80} + 2592 q^{85} - 4296 q^{86} + 2232 q^{89} + 1944 q^{91} + 792 q^{94} - 2784 q^{95} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
45.4.b.a \(2\) \(2.655\) \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}+3q^{4}+5\beta q^{5}+11\beta q^{8}-5^{2}q^{10}+\cdots\)
45.4.b.b \(4\) \(2.655\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(-6\) \(0\) \(q-\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)