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Properties

Label 1445.2.l
Level $1445$
Weight $2$
Character orbit 1445.l
Rep. character $\chi_{1445}(1001,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $360$
Sturm bound $306$

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Defining parameters

Level: \( N \) \(=\) \( 1445 = 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1445.l (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(306\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1445, [\chi])\).

Total New Old
Modular forms 688 360 328
Cusp forms 544 360 184
Eisenstein series 144 0 144

Trace form

\( 360 q + 8 q^{6} + 24 q^{9} + O(q^{10}) \) \( 360 q + 8 q^{6} + 24 q^{9} + 8 q^{11} - 24 q^{12} + 8 q^{15} - 360 q^{16} - 40 q^{18} + 8 q^{19} + 32 q^{22} + 16 q^{23} + 8 q^{24} - 16 q^{26} - 24 q^{27} - 48 q^{28} + 8 q^{29} + 32 q^{33} + 32 q^{35} + 24 q^{36} - 24 q^{37} - 8 q^{39} - 16 q^{40} - 16 q^{41} + 24 q^{42} - 8 q^{43} - 16 q^{44} - 16 q^{45} - 8 q^{46} - 80 q^{48} - 8 q^{50} + 48 q^{52} - 24 q^{53} + 32 q^{54} - 64 q^{56} - 32 q^{57} + 64 q^{58} - 32 q^{59} - 24 q^{60} - 32 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 96 q^{66} - 192 q^{69} + 24 q^{71} + 64 q^{74} + 8 q^{75} + 8 q^{76} - 24 q^{77} + 112 q^{78} + 32 q^{80} + 80 q^{82} + 96 q^{83} + 208 q^{84} + 48 q^{87} + 8 q^{88} + 24 q^{91} - 80 q^{92} - 64 q^{93} - 56 q^{94} + 16 q^{95} + 168 q^{96} + 40 q^{97} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1445, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1445, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1445, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)