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Properties

Label 900.4.n
Level $900$
Weight $4$
Character orbit 900.n
Rep. character $\chi_{900}(181,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $148$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 900.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

Total New Old
Modular forms 2208 148 2060
Cusp forms 2112 148 1964
Eisenstein series 96 0 96

Trace form

\( 148 q + 7 q^{5} - 8 q^{7} + O(q^{10}) \) \( 148 q + 7 q^{5} - 8 q^{7} - 64 q^{11} + 22 q^{13} - 82 q^{17} + 74 q^{19} + 78 q^{23} + 401 q^{25} - 156 q^{29} - 450 q^{31} - 354 q^{35} + 231 q^{37} - 358 q^{41} - 468 q^{43} - 442 q^{47} + 6624 q^{49} - 1353 q^{53} + 658 q^{55} + 432 q^{59} - 192 q^{61} + 1635 q^{65} - 2630 q^{67} + 1986 q^{71} + 994 q^{73} + 1200 q^{77} - 232 q^{79} + 118 q^{83} + 2139 q^{85} + 1937 q^{89} + 124 q^{91} - 900 q^{95} + 2140 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)