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Properties

Label 152.8.q
Level $152$
Weight $8$
Character orbit 152.q
Rep. character $\chi_{152}(9,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $210$
Sturm bound $160$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 152.q (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(152, [\chi])\).

Total New Old
Modular forms 864 210 654
Cusp forms 816 210 606
Eisenstein series 48 0 48

Trace form

\( 210 q + 39 q^{3} - 5031 q^{9} + O(q^{10}) \) \( 210 q + 39 q^{3} - 5031 q^{9} - 5298 q^{13} + 10668 q^{15} + 31002 q^{17} - 28734 q^{19} + 20574 q^{21} - 3444 q^{23} + 197652 q^{25} + 269241 q^{27} + 398652 q^{29} - 141366 q^{31} - 803835 q^{33} + 41814 q^{35} + 1508004 q^{37} + 931356 q^{39} - 632937 q^{41} - 2397744 q^{43} - 486342 q^{45} + 887040 q^{47} - 11528019 q^{49} - 5516589 q^{51} + 1541466 q^{53} - 2077956 q^{55} + 150972 q^{57} + 3626565 q^{59} - 4567506 q^{61} - 20540358 q^{63} - 6404250 q^{65} + 10780095 q^{67} - 7884216 q^{69} - 414090 q^{71} - 17567238 q^{73} - 35437500 q^{75} - 11531988 q^{77} + 1245036 q^{79} + 43797363 q^{81} + 18835200 q^{83} + 32467452 q^{85} - 22408362 q^{87} - 26851572 q^{89} - 58933980 q^{91} - 10609002 q^{93} - 24197262 q^{95} + 1723197 q^{97} + 56832825 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(152, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)