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Properties

Label 3675.2.da
Level $3675$
Weight $2$
Character orbit 3675.da
Rep. character $\chi_{3675}(82,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $4032$
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.da (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 13728 4032 9696
Cusp forms 13152 4032 9120
Eisenstein series 576 0 576

Trace form

\( 4032 q + 8 q^{7} - 24 q^{8} + O(q^{10}) \) \( 4032 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 368 q^{16} + 28 q^{17} + 4 q^{21} - 20 q^{22} - 16 q^{23} - 64 q^{26} - 24 q^{28} + 48 q^{31} + 192 q^{32} - 36 q^{33} + 672 q^{36} + 12 q^{37} + 12 q^{38} + 224 q^{41} + 16 q^{42} + 24 q^{43} + 16 q^{46} - 144 q^{47} + 208 q^{51} - 108 q^{52} + 576 q^{56} - 16 q^{58} - 44 q^{61} + 4 q^{63} + 144 q^{66} - 8 q^{67} + 132 q^{68} + 352 q^{71} + 96 q^{72} + 36 q^{73} + 60 q^{77} - 80 q^{78} - 336 q^{81} - 128 q^{82} + 224 q^{83} + 32 q^{86} - 52 q^{87} + 584 q^{88} + 204 q^{91} + 8 q^{92} + 628 q^{98} + O(q^{100}) \)

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

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