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Properties

Label 1900.3.bi
Level $1900$
Weight $3$
Character orbit 1900.bi
Rep. character $\chi_{1900}(401,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $378$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.bi (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 3708 378 3330
Cusp forms 3492 378 3114
Eisenstein series 216 0 216

Trace form

\( 378 q - 6 q^{3} - 9 q^{7} + 6 q^{9} + O(q^{10}) \) \( 378 q - 6 q^{3} - 9 q^{7} + 6 q^{9} + 15 q^{11} + 51 q^{13} + 9 q^{17} + 18 q^{19} - 99 q^{21} - 108 q^{23} - 198 q^{27} - 99 q^{29} - 108 q^{31} + 75 q^{33} + 96 q^{39} + 78 q^{41} - 81 q^{43} + 291 q^{47} - 1134 q^{49} - 72 q^{51} + 51 q^{53} - 372 q^{57} - 135 q^{59} + 282 q^{61} - 411 q^{63} + 225 q^{67} - 351 q^{69} + 186 q^{71} - 294 q^{73} - 144 q^{77} - 45 q^{79} - 222 q^{81} - 111 q^{83} - 624 q^{87} + 84 q^{89} - 72 q^{91} + 312 q^{93} - 381 q^{97} - 699 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)