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Properties

Label 3675.2.v
Level $3675$
Weight $2$
Character orbit 3675.v
Rep. character $\chi_{3675}(526,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1068$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.v (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3675, [\chi])\).

Total New Old
Modular forms 3432 1068 2364
Cusp forms 3288 1068 2220
Eisenstein series 144 0 144

Trace form

\( 1068 q - 2 q^{3} - 180 q^{4} + 2 q^{6} + 2 q^{7} + 12 q^{8} - 178 q^{9} + O(q^{10}) \) \( 1068 q - 2 q^{3} - 180 q^{4} + 2 q^{6} + 2 q^{7} + 12 q^{8} - 178 q^{9} - 2 q^{11} - 6 q^{12} - 12 q^{13} + 14 q^{14} - 168 q^{16} - 18 q^{17} - 52 q^{19} - 8 q^{21} - 30 q^{22} + 16 q^{23} + 36 q^{24} - 24 q^{26} - 2 q^{27} + 48 q^{28} - 72 q^{31} - 80 q^{32} + 8 q^{33} - 92 q^{34} - 180 q^{36} + 34 q^{37} + 28 q^{38} + 40 q^{39} + 16 q^{41} + 30 q^{42} + 12 q^{43} - 84 q^{44} + 8 q^{46} + 18 q^{47} + 100 q^{48} - 24 q^{49} - 20 q^{51} + 82 q^{52} - 4 q^{53} + 2 q^{54} - 54 q^{56} - 20 q^{57} - 2 q^{58} + 40 q^{61} + 52 q^{62} + 16 q^{63} - 248 q^{64} + 32 q^{66} + 24 q^{67} - 12 q^{68} + 8 q^{69} - 84 q^{71} - 30 q^{72} + 38 q^{73} + 8 q^{74} - 34 q^{76} + 42 q^{77} - 52 q^{78} - 40 q^{79} - 178 q^{81} - 28 q^{82} - 22 q^{83} - 18 q^{84} - 4 q^{86} - 10 q^{87} - 100 q^{88} + 102 q^{89} + 114 q^{91} + 26 q^{92} - 20 q^{93} + 166 q^{94} + 94 q^{96} - 100 q^{97} - 224 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)