Space of modular forms of level 1904, weight 2, and Character 1904.c

• Label: 1904.2.c
• Level: $1904$
• Weight: $2$
• Character orbit: 1904.c
• Rep. character: $\chi_{1904}(1121,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $9$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1904.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1904, [\chi])\).

	Total	New	Old
Modular forms	300	54	246
Cusp forms	276	54	222
Eisenstein series	24	0	24

Trace form

\( 54 q - 62 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1904, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1904.2.c.a	$1904$	$2$	1904.c	17.b	$2$	$2$	$2$	$15.204$	\(\Q(\sqrt{-1}) \)	None					952.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-2iq^{5}-iq^{7}-q^{9}+2iq^{11}+\cdots\)
1904.2.c.b	$1904$	$2$	1904.c	17.b	$2$	$2$	$2$	$15.204$	\(\Q(\sqrt{-1}) \)	None					238.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{9}+2q^{13}+(1-4i)q^{17}+\cdots\)
1904.2.c.c	$1904$	$2$	1904.c	17.b	$2$	$4$	$4$	$15.204$	\(\Q(i, \sqrt{29})\)	None					952.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-5+\cdots)q^{9}+\cdots\)
1904.2.c.d	$1904$	$2$	1904.c	17.b	$2$	$4$	$4$	$15.204$	\(\Q(i, \sqrt{13})\)	None					952.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+(-4+\cdots)q^{9}+\cdots\)
1904.2.c.e	$1904$	$2$	1904.c	17.b	$2$	$6$	$6$	$15.204$	6.0.350464.1	None					238.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1904.2.c.f	$1904$	$2$	1904.c	17.b	$2$	$8$	$8$	$15.204$	8.0.980441344.2	None					476.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}+\beta _{7})q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1904.2.c.g	$1904$	$2$	1904.c	17.b	$2$	$8$	$8$	$15.204$	8.0.6179217664.1	None					952.2.c.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{5}-\beta _{6})q^{3}+(\beta _{5}+\beta _{7})q^{5}-\beta _{5}q^{7}+\cdots\)
1904.2.c.h	$1904$	$2$	1904.c	17.b	$2$	$10$	$10$	$15.204$	10.0.\(\cdots\).1	None					952.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+(-\beta _{4}-\beta _{6}-\beta _{7}+\beta _{8}+\beta _{9})q^{5}+\cdots\)
1904.2.c.i	$1904$	$2$	1904.c	17.b	$2$	$10$	$10$	$15.204$	10.0.\(\cdots\).1	None					119.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}+(\beta _{5}-\beta _{7})q^{5}-\beta _{7}q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1904, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1904, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(952, [\chi])\)\(^{\oplus 2}\)