Space of modular forms of level 350, weight 4, and Character 350.o

• Label: 350.4.o
• Level: $350$
• Weight: $4$
• Character orbit: 350.o
• Rep. character: $\chi_{350}(143,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $144$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(350, [\chi])\).

	Total	New	Old
Modular forms	768	144	624
Cusp forms	672	144	528
Eisenstein series	96	0	96

Trace form

144 * q + 4 * q^7 - 88 * q^11 + 1152 * q^16 - 288 * q^17 - 16 * q^18 + 648 * q^21 - 624 * q^22 + 252 * q^23 - 912 * q^26 - 112 * q^28 + 1056 * q^31 + 1956 * q^33 - 3712 * q^36 + 552 * q^37 + 528 * q^38 + 488 * q^42 - 2176 * q^43 - 1792 * q^46 - 1464 * q^47 + 336 * q^51 - 576 * q^53 - 576 * q^56 + 224 * q^57 - 1024 * q^58 - 2808 * q^61 - 3972 * q^63 + 1936 * q^67 - 1152 * q^68 + 1344 * q^71 - 64 * q^72 + 5616 * q^73 + 6908 * q^77 + 4192 * q^78 - 3080 * q^81 - 864 * q^82 - 1552 * q^86 - 15732 * q^87 - 1248 * q^88 - 10944 * q^91 - 2016 * q^92 - 144 * q^93 + 768 * q^96 + 400 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)