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Properties

Label 45.18.l
Level $45$
Weight $18$
Character orbit 45.l
Rep. character $\chi_{45}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $400$
Sturm bound $108$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 45.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(108\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(45, [\chi])\).

Total New Old
Modular forms 416 416 0
Cusp forms 400 400 0
Eisenstein series 16 16 0

Trace form

\( 400 q - 6 q^{2} - 3606 q^{3} - 6 q^{5} + 9537528 q^{6} - 2 q^{7} + O(q^{10}) \) \( 400 q - 6 q^{2} - 3606 q^{3} - 6 q^{5} + 9537528 q^{6} - 2 q^{7} - 8 q^{10} - 357324768 q^{11} + 685700214 q^{12} - 2 q^{13} + 14329253634 q^{15} + 807453851644 q^{16} - 178736908704 q^{18} + 826651705338 q^{20} + 458167880604 q^{21} - 524290 q^{22} + 1141152819858 q^{23} - 121151473496 q^{25} - 10775198387502 q^{27} - 68718952456 q^{28} + 15566248814670 q^{30} - 4 q^{31} - 10328468613450 q^{32} + 35039958744048 q^{33} - 67956422210232 q^{36} - 27943159668356 q^{37} + 126839272774650 q^{38} + 34359738366 q^{40} + 66336392889624 q^{41} - 180606225827814 q^{42} - 2 q^{43} - 75442553959176 q^{45} - 943979328083080 q^{46} + 1480630339954428 q^{47} - 1133017997069130 q^{48} - 816704461221894 q^{50} - 2037922410499740 q^{51} - 68719214594 q^{52} - 101877204002176 q^{55} - 2155039425740376 q^{56} - 102016329270666 q^{57} + 308594228458494 q^{58} + 12574085279140938 q^{60} - 2571006081740920 q^{61} - 38843820277284 q^{63} + 24232044460613826 q^{65} - 20973157504988676 q^{66} - 3984437294820476 q^{67} + 35298532293869562 q^{68} + 3051757812498 q^{70} - 64540265153600862 q^{72} - 8 q^{73} + 8404703928159642 q^{75} - 3336551780530344 q^{76} - 137823076030206246 q^{77} - 14710249398166902 q^{78} + 16269722055506472 q^{81} - 30151562932244488 q^{82} - 119811454225444866 q^{83} - 56191618494117098 q^{85} + 536612112428109936 q^{86} + 188624594154215262 q^{87} + 57789034794399318 q^{88} - 3997368164616486 q^{90} - 120675100055944744 q^{91} + 751929099416598000 q^{92} + 325562468445876942 q^{93} - 238443974054182116 q^{95} - 877105122817737468 q^{96} + 177621748221558928 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

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