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Properties

Label 102.5.g
Level $102$
Weight $5$
Character orbit 102.g
Rep. character $\chi_{102}(53,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $96$
Newform subspaces $4$
Sturm bound $90$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 102.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 4 \)
Sturm bound: \(90\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(102, [\chi])\).

Total New Old
Modular forms 304 96 208
Cusp forms 272 96 176
Eisenstein series 32 0 32

Trace form

\( 96 q - 112 q^{9} + O(q^{10}) \) \( 96 q - 112 q^{9} + 512 q^{10} - 128 q^{12} - 1096 q^{15} - 6144 q^{16} + 1024 q^{18} - 512 q^{24} + 1792 q^{25} - 2400 q^{27} - 2832 q^{31} - 256 q^{33} - 3328 q^{34} + 896 q^{36} + 4992 q^{37} - 5104 q^{39} + 3840 q^{42} + 3408 q^{43} + 18584 q^{45} + 6144 q^{46} + 26464 q^{49} - 17168 q^{51} - 3200 q^{52} - 18752 q^{54} - 14168 q^{57} - 9216 q^{58} - 8768 q^{60} - 176 q^{61} + 26344 q^{63} + 7936 q^{66} + 8960 q^{67} + 4288 q^{69} - 3328 q^{70} + 5920 q^{73} + 70104 q^{75} - 9728 q^{78} - 8256 q^{79} + 14848 q^{82} - 13312 q^{84} - 54160 q^{85} + 10376 q^{87} + 31744 q^{88} - 29184 q^{90} + 112480 q^{91} - 8808 q^{93} + 34048 q^{94} - 49488 q^{97} + 61280 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(102, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
102.5.g.a 102.g 51.g $4$ $10.544$ \(\Q(\zeta_{8})\) None \(-8\) \(24\) \(8\) \(-132\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-2-2\zeta_{8}^{2})q^{2}+(6+3\zeta_{8}-6\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
102.5.g.b 102.g 51.g $4$ $10.544$ \(\Q(\zeta_{8})\) None \(8\) \(12\) \(-8\) \(-132\) $\mathrm{SU}(2)[C_{8}]$ \(q+(2+2\zeta_{8}^{2})q^{2}+(3+6\zeta_{8}+6\zeta_{8}^{3})q^{3}+\cdots\)
102.5.g.c 102.g 51.g $44$ $10.544$ None \(-88\) \(-32\) \(-72\) \(132\) $\mathrm{SU}(2)[C_{8}]$
102.5.g.d 102.g 51.g $44$ $10.544$ None \(88\) \(-4\) \(72\) \(132\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{5}^{\mathrm{old}}(102, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(102, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)