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Properties

Label 150.11.k
Level $150$
Weight $11$
Character orbit 150.k
Rep. character $\chi_{150}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $400$
Sturm bound $330$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 150.k (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(330\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(150, [\chi])\).

Total New Old
Modular forms 2432 400 2032
Cusp forms 2368 400 1968
Eisenstein series 64 0 64

Trace form

\( 400 q - 64 q^{2} + 15120 q^{5} + 2816 q^{7} + 32768 q^{8} + O(q^{10}) \) \( 400 q - 64 q^{2} + 15120 q^{5} + 2816 q^{7} + 32768 q^{8} - 102464 q^{10} - 769932 q^{13} + 662904 q^{15} + 26214400 q^{16} - 12289444 q^{17} + 5038848 q^{18} - 4829000 q^{19} - 6381568 q^{20} + 24178176 q^{22} + 63843936 q^{23} + 49952228 q^{25} + 43715200 q^{26} + 45641728 q^{28} + 341738000 q^{29} + 79377408 q^{30} - 67108864 q^{32} - 121758552 q^{33} + 116632000 q^{34} + 615188552 q^{35} - 1007769600 q^{36} + 795043908 q^{37} - 35204096 q^{38} + 2588672 q^{40} - 207488800 q^{41} + 143016192 q^{42} - 1099153968 q^{43} - 61332228 q^{45} + 2818936384 q^{47} - 817307072 q^{50} - 394205184 q^{52} - 3303590860 q^{53} + 4210843728 q^{55} + 934010352 q^{57} + 1151328256 q^{58} - 7071044000 q^{59} - 645967872 q^{60} + 2082529200 q^{61} - 4455320320 q^{62} + 55427328 q^{63} - 3262614676 q^{65} - 9903237504 q^{67} - 2442586112 q^{68} + 8053417472 q^{70} - 644972544 q^{72} + 5669529788 q^{73} + 1946912112 q^{75} + 2118642848 q^{77} + 1771559424 q^{78} - 8263862000 q^{79} - 3963617280 q^{80} + 38742048900 q^{81} + 27663164928 q^{82} - 29160545792 q^{83} + 14061048832 q^{85} + 31233338208 q^{87} + 6915227648 q^{88} - 4481679500 q^{89} - 99517248 q^{90} - 15103664128 q^{92} - 13446659664 q^{93} + 6269022016 q^{95} + 46150384148 q^{97} + 49552897984 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{11}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)