Properties

Label 45.4.e
Level $45$
Weight $4$
Character orbit 45.e
Rep. character $\chi_{45}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $3$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
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 40 24 16
Cusp forms 32 24 8
Eisenstein series 8 0 8

Trace form

\( 24 q + 4 q^{2} - 2 q^{3} - 48 q^{4} + 10 q^{5} + 2 q^{6} + 12 q^{7} - 108 q^{8} - 16 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{2} - 2 q^{3} - 48 q^{4} + 10 q^{5} + 2 q^{6} + 12 q^{7} - 108 q^{8} - 16 q^{9} + 46 q^{11} + 314 q^{12} - 24 q^{13} - 6 q^{14} - 20 q^{15} - 192 q^{16} - 500 q^{17} + 40 q^{18} + 300 q^{19} + 120 q^{20} - 36 q^{22} + 192 q^{23} + 12 q^{24} - 300 q^{25} + 1432 q^{26} + 124 q^{27} - 384 q^{28} - 286 q^{29} - 220 q^{30} + 120 q^{31} - 484 q^{32} - 1222 q^{33} + 378 q^{34} - 560 q^{35} - 1142 q^{36} + 336 q^{37} + 88 q^{38} - 320 q^{39} + 90 q^{40} - 472 q^{41} + 2670 q^{42} + 174 q^{43} + 1652 q^{44} + 740 q^{45} + 540 q^{46} + 400 q^{47} + 452 q^{48} - 1026 q^{49} + 100 q^{50} + 1106 q^{51} - 1302 q^{52} - 2024 q^{53} - 2428 q^{54} - 1530 q^{56} - 254 q^{57} - 594 q^{58} + 298 q^{59} + 170 q^{60} + 858 q^{61} - 1644 q^{62} + 1728 q^{63} + 2760 q^{64} + 840 q^{65} + 3076 q^{66} + 1362 q^{67} + 2732 q^{68} - 3234 q^{69} + 180 q^{70} + 272 q^{71} - 3960 q^{72} + 1812 q^{73} - 1480 q^{74} - 50 q^{75} - 2598 q^{76} + 1056 q^{77} - 5518 q^{78} - 888 q^{79} - 4560 q^{80} - 2284 q^{81} - 3492 q^{82} + 2508 q^{83} + 4902 q^{84} - 360 q^{85} - 2762 q^{86} + 6280 q^{87} - 432 q^{88} + 7404 q^{89} + 1330 q^{90} + 3984 q^{91} + 4140 q^{92} + 1464 q^{93} + 1962 q^{94} + 2040 q^{95} + 586 q^{96} - 474 q^{97} + 2696 q^{98} + 1468 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.4.e.a 45.e 9.c $4$ $2.655$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(1\) \(-6\) \(-10\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots\)
45.4.e.b 45.e 9.c $6$ $2.655$ 6.0.15759792.1 None \(1\) \(9\) \(-15\) \(43\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}+(1+\beta _{2}-\beta _{5})q^{3}+\cdots\)
45.4.e.c 45.e 9.c $14$ $2.655$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(-5\) \(35\) \(-22\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(\beta _{7}-\beta _{10})q^{3}+(-5+\cdots)q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)