Space of modular forms of level 1904, weight 2, and trivial character

• Label: 1904.2.a
• Level: $1904$
• Weight: $2$
• Character orbit: 1904.a
• Rep. character: $\chi_{1904}(1,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $20$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1904.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1904))\).

	Total	New	Old
Modular forms	300	48	252
Cusp forms	277	48	229
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.

\(2\)	\(7\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(9\)
Plus space			\(+\)	\(19\)
Minus space			\(-\)	\(29\)

Trace form

48 * q + 2 * q^7 + 48 * q^9 - 8 * q^11 - 24 * q^15 + 16 * q^23 + 48 * q^25 - 8 * q^29 - 8 * q^37 + 40 * q^39 + 36 * q^43 - 24 * q^47 + 48 * q^49 - 12 * q^51 - 8 * q^53 + 8 * q^55 + 16 * q^57 + 24 * q^59 + 10 * q^63 + 16 * q^65 - 4 * q^67 + 32 * q^71 + 64 * q^75 - 8 * q^77 + 40 * q^79 + 64 * q^81 + 40 * q^83 + 56 * q^87 + 16 * q^89 - 12 * q^91 - 48 * q^93 + 48 * q^95 + 16 * q^97 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1904))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	17
1904.2.a.a	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	\(\Q\)	None	✓				238.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
1904.2.a.b	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	\(\Q\)	None	✓				238.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
1904.2.a.c	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	\(\Q\)	None	✓				238.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-3q^{9}+2q^{11}-q^{17}+\cdots\)
1904.2.a.d	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	\(\Q\)	None	✓				238.2.a.d	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots\)
1904.2.a.e	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	\(\Q\)	None	✓				238.2.a.c	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
1904.2.a.f	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{5}) \)	None	✓				238.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1904.2.a.g	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{13}) \)	None	✓				952.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
1904.2.a.h	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{13}) \)	None	✓		✓		476.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
1904.2.a.i	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{5}) \)	None	✓				952.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
1904.2.a.j	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{5}) \)	None	✓				476.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
1904.2.a.k	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{13}) \)	None	✓		✓		476.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}-4q^{11}+\cdots\)
1904.2.a.l	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	\(\Q(\sqrt{13}) \)	None	✓				476.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
1904.2.a.m	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.229.1	None	✓				952.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
1904.2.a.n	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.1229.1	None	✓				952.2.a.e	$1$	$0$	\(0\)	\(1\)	\(3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1904.2.a.o	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.229.1	None	✓				952.2.a.c	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-2-\beta _{2})q^{5}-q^{7}+\cdots\)
1904.2.a.p	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.229.1	None	✓				952.2.a.d	$1$	$0$	\(0\)	\(3\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1904.2.a.q	$1904$	$2$	1904.a	1.a	$1$	$4$	$4$	$15.204$	4.4.5225.1	None	✓		✓		952.2.a.g	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+q^{7}+\cdots\)
1904.2.a.r	$1904$	$2$	1904.a	1.a	$1$	$4$	$4$	$15.204$	4.4.13448.1	None	✓		✓		952.2.a.h	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
1904.2.a.s	$1904$	$2$	1904.a	1.a	$1$	$4$	$4$	$15.204$	4.4.9301.1	None	✓		✓		119.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-\beta _{2}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1904.2.a.t	$1904$	$2$	1904.a	1.a	$1$	$5$	$5$	$15.204$	5.5.453749.1	None	✓		✓		119.2.a.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1904)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 2}\)