Space of modular forms of level 1900, weight 2, and Character 1900.bn

• Label: 1900.2.bn
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.bn
• Rep. character: $\chi_{1900}(51,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $1104$
• Sturm bound: $600$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.bn (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

	Total	New	Old
Modular forms	1872	1176	696
Cusp forms	1728	1104	624
Eisenstein series	144	72	72

Trace form

1104 * q + 6 * q^2 - 12 * q^6 + 9 * q^8 + 6 * q^9 + 9 * q^12 + 24 * q^13 - 21 * q^14 - 24 * q^16 + 12 * q^17 - 6 * q^21 + 12 * q^22 + 12 * q^24 - 33 * q^26 + 12 * q^29 + 51 * q^32 + 24 * q^33 + 60 * q^34 + 9 * q^36 - 30 * q^38 - 18 * q^41 + 51 * q^42 + 81 * q^44 + 18 * q^46 - 27 * q^48 + 450 * q^49 - 3 * q^52 - 39 * q^54 + 12 * q^57 - 60 * q^58 - 24 * q^61 - 6 * q^62 + 9 * q^64 - 90 * q^66 - 36 * q^68 - 126 * q^69 + 162 * q^72 + 12 * q^73 + 69 * q^74 - 66 * q^76 + 36 * q^77 - 63 * q^78 + 12 * q^81 + 141 * q^82 + 117 * q^84 - 84 * q^86 - 63 * q^88 - 24 * q^89 + 48 * q^92 + 18 * q^93 - 186 * q^96 + 18 * q^97 + 81 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)