Space of modular forms of level 2300 and weight 2

• Label: 2300.2
• Level: 2300
• Weight: 2
• Dimension: 83978
• Nonzero newspaces: 24
• Sturm bound: 633600
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(633600\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2300))\).

	Total	New	Old
Modular forms	161480	85702	75778
Cusp forms	155321	83978	71343
Eisenstein series	6159	1724	4435

Trace form

83978 * q - 131 * q^2 - 8 * q^3 - 123 * q^4 - 322 * q^5 - 195 * q^6 + 8 * q^7 - 107 * q^8 - 242 * q^9 - 144 * q^10 - 123 * q^12 - 246 * q^13 - 123 * q^14 + 4 * q^15 - 227 * q^16 - 237 * q^17 - 147 * q^18 + 13 * q^19 - 164 * q^20 - 399 * q^21 - 112 * q^22 + 10 * q^23 - 286 * q^24 - 238 * q^25 - 379 * q^26 + 43 * q^27 - 123 * q^28 - 193 * q^29 - 156 * q^30 + 13 * q^31 - 91 * q^32 - 217 * q^33 - 101 * q^34 + 16 * q^35 - 156 * q^36 - 260 * q^37 - 128 * q^38 - 52 * q^39 - 264 * q^40 - 448 * q^41 - 213 * q^42 - 76 * q^43 - 186 * q^44 - 462 * q^45 - 185 * q^46 - 60 * q^47 - 295 * q^48 - 322 * q^49 - 364 * q^50 - 28 * q^51 - 209 * q^52 - 266 * q^53 - 295 * q^54 - 80 * q^55 - 260 * q^56 - 363 * q^57 - 176 * q^58 - 34 * q^59 - 356 * q^60 - 330 * q^61 - 223 * q^62 - 27 * q^63 - 183 * q^64 - 222 * q^65 - 324 * q^66 + 66 * q^67 - 160 * q^68 - 275 * q^69 - 332 * q^70 - 23 * q^71 - 78 * q^72 - 268 * q^73 - 154 * q^74 + 156 * q^75 - 386 * q^76 - 53 * q^77 - 293 * q^78 + 90 * q^79 - 124 * q^80 - 482 * q^81 - 45 * q^82 + 113 * q^83 - 117 * q^84 - 406 * q^85 - 185 * q^86 + 38 * q^87 + 29 * q^88 - 374 * q^89 + 156 * q^90 + 20 * q^91 - 132 * q^92 - 456 * q^93 + 120 * q^94 - 28 * q^95 - 204 * q^96 - 277 * q^97 + 85 * q^98 + 331 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2300))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
2300.2.a	\(\chi_{2300}(1, \cdot)\)	2300.2.a.a	1	1
		2300.2.a.b	1
		2300.2.a.c	1
		2300.2.a.d	1
		2300.2.a.e	1
		2300.2.a.f	1
		2300.2.a.g	1
		2300.2.a.h	1
		2300.2.a.i	2
		2300.2.a.j	3
		2300.2.a.k	3
		2300.2.a.l	4
		2300.2.a.m	4
		2300.2.a.n	6
		2300.2.a.o	6
2300.2.c	\(\chi_{2300}(1749, \cdot)\)	2300.2.c.a	2	1
		2300.2.c.b	2
		2300.2.c.c	2
		2300.2.c.d	2
		2300.2.c.e	2
		2300.2.c.f	2
		2300.2.c.g	2
		2300.2.c.h	4
		2300.2.c.i	6
		2300.2.c.j	8
2300.2.e	\(\chi_{2300}(551, \cdot)\)	n/a	222	1
2300.2.g	\(\chi_{2300}(2299, \cdot)\)	n/a	212	1
2300.2.i	\(\chi_{2300}(1057, \cdot)\)	2300.2.i.a	8	2
		2300.2.i.b	8
		2300.2.i.c	8
		2300.2.i.d	16
		2300.2.i.e	16
		2300.2.i.f	16
2300.2.j	\(\chi_{2300}(507, \cdot)\)	n/a	396	2
2300.2.m	\(\chi_{2300}(461, \cdot)\)	n/a	216	4
2300.2.n	\(\chi_{2300}(459, \cdot)\)	n/a	1424	4
2300.2.q	\(\chi_{2300}(369, \cdot)\)	n/a	224	4
2300.2.s	\(\chi_{2300}(91, \cdot)\)	n/a	1424	4
2300.2.u	\(\chi_{2300}(101, \cdot)\)	n/a	380	10
2300.2.x	\(\chi_{2300}(47, \cdot)\)	n/a	2640	8
2300.2.y	\(\chi_{2300}(137, \cdot)\)	n/a	480	8
2300.2.ba	\(\chi_{2300}(99, \cdot)\)	n/a	2120	10
2300.2.bc	\(\chi_{2300}(51, \cdot)\)	n/a	2220	10
2300.2.be	\(\chi_{2300}(49, \cdot)\)	n/a	360	10
2300.2.bi	\(\chi_{2300}(243, \cdot)\)	n/a	4240	20
2300.2.bj	\(\chi_{2300}(57, \cdot)\)	n/a	720	20
2300.2.bk	\(\chi_{2300}(41, \cdot)\)	n/a	2400	40
2300.2.bm	\(\chi_{2300}(11, \cdot)\)	n/a	14240	40
2300.2.bo	\(\chi_{2300}(9, \cdot)\)	n/a	2400	40
2300.2.br	\(\chi_{2300}(19, \cdot)\)	n/a	14240	40
2300.2.bs	\(\chi_{2300}(17, \cdot)\)	n/a	4800	80
2300.2.bt	\(\chi_{2300}(3, \cdot)\)	n/a	28480	80

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)\(^{\oplus 2}\)