Space of modular forms of level 400, weight 4, and Character 400.y

• Label: 400.4.y
• Level: $400$
• Weight: $4$
• Character orbit: 400.y
• Rep. character: $\chi_{400}(129,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $176$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).

	Total	New	Old
Modular forms	744	184	560
Cusp forms	696	176	520
Eisenstein series	48	8	40

Trace form

176 * q + 5 * q^3 - 5 * q^5 + 375 * q^9 + 69 * q^11 - 5 * q^13 + 37 * q^15 - 5 * q^17 - 111 * q^19 + 78 * q^21 - 205 * q^23 - 77 * q^25 + 5 * q^27 - 145 * q^29 - 183 * q^31 - 5 * q^33 - 556 * q^35 + 820 * q^37 + 369 * q^39 - 121 * q^41 + 139 * q^45 + 5 * q^47 - 7864 * q^49 - 2386 * q^51 - 720 * q^53 - 1051 * q^55 - 1059 * q^59 + 387 * q^61 - 1710 * q^63 - 986 * q^65 - 2305 * q^67 - 57 * q^69 - 991 * q^71 - 5 * q^73 + 2693 * q^75 + 1710 * q^77 + 793 * q^79 - 3429 * q^81 - 5185 * q^83 + 1682 * q^85 - 3415 * q^87 - 168 * q^89 + 66 * q^91 + 3063 * q^95 + 1855 * q^97 + 5732 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(400, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(400, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)