Space of modular forms of level 3675, weight 2, and Character 3675.n

• Label: 3675.2.n
• Level: $3675$
• Weight: $2$
• Character orbit: 3675.n
• Rep. character: $\chi_{3675}(736,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $824$
• Sturm bound: $1120$

Defining parameters

Level:	\( N \)	\(=\)	\( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3675.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(1120\)

Dimensions

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

	Total	New	Old
Modular forms	2304	824	1480
Cusp forms	2176	824	1352
Eisenstein series	128	0	128

Trace form

824 * q - 2 * q^2 - 208 * q^4 - 2 * q^5 + 2 * q^6 - 24 * q^8 - 206 * q^9 + 2 * q^10 - 6 * q^11 - 8 * q^12 - 12 * q^13 - 200 * q^16 - 22 * q^17 + 8 * q^18 + 14 * q^19 + 44 * q^20 + 14 * q^22 - 36 * q^23 - 24 * q^24 + 16 * q^25 - 32 * q^26 - 28 * q^29 - 52 * q^30 + 6 * q^31 + 60 * q^32 + 18 * q^33 + 42 * q^34 - 208 * q^36 + 32 * q^37 - 30 * q^38 - 8 * q^39 + 84 * q^40 - 42 * q^41 - 72 * q^43 + 58 * q^44 - 2 * q^45 + 64 * q^47 - 54 * q^50 + 32 * q^51 - 128 * q^52 + 84 * q^53 + 2 * q^54 + 54 * q^55 - 42 * q^58 - 36 * q^59 - 10 * q^60 + 12 * q^61 + 14 * q^62 - 190 * q^64 + 48 * q^65 - 8 * q^67 - 4 * q^68 + 4 * q^69 + 40 * q^71 - 24 * q^72 - 40 * q^73 - 32 * q^74 - 8 * q^75 - 104 * q^76 + 40 * q^78 + 4 * q^79 + 2 * q^80 - 206 * q^81 - 60 * q^82 - 42 * q^83 + 194 * q^85 + 84 * q^86 + 40 * q^87 - 120 * q^88 + 48 * q^89 - 28 * q^90 + 58 * q^92 - 104 * q^93 + 6 * q^94 + 12 * q^95 - 26 * q^96 - 12 * q^97 + 4 * q^99

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

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)