Properties

Label 45.6.b
Level $45$
Weight $6$
Character orbit 45.b
Rep. character $\chi_{45}(19,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $36$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 45.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(45, [\chi])\).

Total New Old
Modular forms 34 14 20
Cusp forms 26 12 14
Eisenstein series 8 2 6

Trace form

\( 12 q - 204 q^{4} - 30 q^{5} + O(q^{10}) \) \( 12 q - 204 q^{4} - 30 q^{5} - 360 q^{10} - 840 q^{11} + 2316 q^{14} + 6996 q^{16} - 4032 q^{19} + 180 q^{20} - 2040 q^{25} - 5772 q^{26} + 6756 q^{29} - 11664 q^{31} - 27912 q^{34} - 25320 q^{35} + 69900 q^{40} - 3228 q^{41} + 96084 q^{44} + 22488 q^{46} - 69972 q^{49} - 93000 q^{50} + 88200 q^{55} - 78780 q^{56} + 163992 q^{59} + 83376 q^{61} - 369324 q^{64} - 82680 q^{65} + 72720 q^{70} - 141552 q^{71} + 282276 q^{74} + 298824 q^{76} - 39456 q^{79} - 180060 q^{80} + 12780 q^{85} - 57120 q^{86} + 293508 q^{89} + 147888 q^{91} - 445680 q^{94} - 99960 q^{95} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.6.b.a 45.b 5.b $2$ $7.217$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-93q^{4}+5\beta q^{5}-61\beta q^{8}+\cdots\)
45.6.b.b 45.b 5.b $2$ $7.217$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(90\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-12q^{4}+(45-5\beta )q^{5}-9\beta q^{7}+\cdots\)
45.6.b.c 45.b 5.b $4$ $7.217$ \(\Q(i, \sqrt{89})\) None \(0\) \(0\) \(-120\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-11+\beta _{3})q^{4}+(-30-5\beta _{1}+\cdots)q^{5}+\cdots\)
45.6.b.d 45.b 5.b $4$ $7.217$ \(\Q(\sqrt{-5}, \sqrt{-14})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+12q^{4}+(5\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)