Space of modular forms of level 19275, weight 2, and trivial character

• Label: 19275.2.a
• Level: $19275$
• Weight: $2$
• Character orbit: 19275.a
• Rep. character: $\chi_{19275}(1,\cdot)$
• Character field: $\Q$
• Dimension: $810$
• Sturm bound: $5160$

Defining parameters

Level:	\( N \)	\(=\)	\( 19275 = 3 \cdot 5^{2} \cdot 257 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19275.a (trivial)
Character field:			\(\Q\)
Sturm bound:			\(5160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(19275))\).

	Total	New	Old
Modular forms	2592	810	1782
Cusp forms	2569	810	1759
Eisenstein series	23	0	23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(5\)	\(257\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(94\)
\(+\)	\(+\)	\(-\)	\(-\)	\(100\)
\(+\)	\(-\)	\(+\)	\(-\)	\(112\)
\(+\)	\(-\)	\(-\)	\(+\)	\(100\)
\(-\)	\(+\)	\(+\)	\(-\)	\(98\)
\(-\)	\(+\)	\(-\)	\(+\)	\(92\)
\(-\)	\(-\)	\(+\)	\(+\)	\(101\)
\(-\)	\(-\)	\(-\)	\(-\)	\(113\)
Plus space			\(+\)	\(387\)
Minus space			\(-\)	\(423\)

Trace form

810 * q - 4 * q^2 - 2 * q^3 + 804 * q^4 + 2 * q^6 - 12 * q^8 + 810 * q^9 + 2 * q^12 - 8 * q^13 + 20 * q^14 + 816 * q^16 - 4 * q^18 + 8 * q^19 - 16 * q^21 - 8 * q^22 + 12 * q^23 - 6 * q^24 + 4 * q^26 - 2 * q^27 - 28 * q^28 - 4 * q^31 - 68 * q^32 + 12 * q^33 - 24 * q^34 + 804 * q^36 - 40 * q^37 - 20 * q^38 - 8 * q^39 + 16 * q^41 - 16 * q^42 + 4 * q^43 - 24 * q^44 - 92 * q^46 - 16 * q^47 - 14 * q^48 + 822 * q^49 + 8 * q^51 - 60 * q^52 - 24 * q^53 + 2 * q^54 - 8 * q^56 - 12 * q^57 + 32 * q^59 - 8 * q^61 - 52 * q^62 + 732 * q^64 + 16 * q^67 + 28 * q^68 + 28 * q^71 - 12 * q^72 + 4 * q^73 - 16 * q^74 + 32 * q^76 + 28 * q^77 - 64 * q^79 + 810 * q^81 - 44 * q^82 + 4 * q^83 - 52 * q^84 - 44 * q^86 + 8 * q^87 - 32 * q^88 + 52 * q^89 - 4 * q^91 - 56 * q^92 - 24 * q^93 + 60 * q^94 - 10 * q^96 - 12 * q^97 - 44 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(19275))\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(19275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(19275)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(257))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(771))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6425))\)\(^{\oplus 2}\)