↑

Properties

Label 2574.2.a
Level $2574$
Weight $2$
Character orbit 2574.a
Rep. character $\chi_{2574}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $36$
Sturm bound $1008$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2574 = 2 \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2574.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(1008\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2574))\).

Total New Old
Modular forms 520 50 470
Cusp forms 489 50 439
Eisenstein series 31 0 31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(11\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(-\)\(+\)\(-\)$+$\(4\)
\(+\)\(-\)\(-\)\(+\)$+$\(2\)
\(+\)\(-\)\(-\)\(-\)$-$\(5\)
\(-\)\(+\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(5\)
\(-\)\(-\)\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(16\)
Minus space\(-\)\(34\)

Trace form

\( 50 q + 50 q^{4} - 8 q^{5} + O(q^{10}) \) \( 50 q + 50 q^{4} - 8 q^{5} - 2 q^{11} - 8 q^{14} + 50 q^{16} - 16 q^{17} + 8 q^{19} - 8 q^{20} + 12 q^{23} + 70 q^{25} - 6 q^{26} + 24 q^{29} + 28 q^{31} + 4 q^{35} + 16 q^{37} + 24 q^{38} + 24 q^{41} + 32 q^{43} - 2 q^{44} + 32 q^{46} + 20 q^{47} + 90 q^{49} + 16 q^{50} - 4 q^{53} + 12 q^{55} - 8 q^{56} - 4 q^{58} + 40 q^{59} + 32 q^{61} + 4 q^{62} + 50 q^{64} + 8 q^{65} + 16 q^{67} - 16 q^{68} + 48 q^{70} - 28 q^{71} - 32 q^{73} + 24 q^{74} + 8 q^{76} + 8 q^{77} - 32 q^{79} - 8 q^{80} - 16 q^{82} + 32 q^{83} + 8 q^{85} - 4 q^{86} - 12 q^{89} + 4 q^{91} + 12 q^{92} + 8 q^{94} + 16 q^{95} + 12 q^{97} - 16 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2574))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11 13
2574.2.a.a 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-4\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-4q^{7}-q^{8}+4q^{10}+\cdots\)
2574.2.a.b 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-q^{11}+\cdots\)
2574.2.a.c 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots\)
2574.2.a.d 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
2574.2.a.e 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
2574.2.a.f 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
2574.2.a.g 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(-1\) \(3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots\)
2574.2.a.h 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{11}+q^{13}+\cdots\)
2574.2.a.i 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(1\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots\)
2574.2.a.j 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2574.2.a.k 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2574.2.a.l 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
2574.2.a.m 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
2574.2.a.n 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(3\) \(-5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-5q^{7}-q^{8}-3q^{10}+\cdots\)
2574.2.a.o 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
2574.2.a.p 2574.a 1.a $1$ $20.553$ \(\Q\) None \(-1\) \(0\) \(3\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+5q^{7}-q^{8}-3q^{10}+\cdots\)
2574.2.a.q 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(-3\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
2574.2.a.r 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(-3\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
2574.2.a.s 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots\)
2574.2.a.t 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots\)
2574.2.a.u 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{7}+q^{8}+q^{11}+q^{13}+\cdots\)
2574.2.a.v 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{11}+q^{13}+\cdots\)
2574.2.a.w 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
2574.2.a.x 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots\)
2574.2.a.y 2574.a 1.a $1$ $20.553$ \(\Q\) None \(1\) \(0\) \(2\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots\)
2574.2.a.z 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{41}) \) None \(-2\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
2574.2.a.ba 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{15}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-\beta q^{7}-q^{8}+q^{10}+\cdots\)
2574.2.a.bb 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots\)
2574.2.a.bc 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(-1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta q^{5}-\beta q^{7}+q^{8}-\beta q^{10}+\cdots\)
2574.2.a.bd 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots\)
2574.2.a.be 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{41}) \) None \(2\) \(0\) \(1\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+(2-\beta )q^{7}+q^{8}+\cdots\)
2574.2.a.bf 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{15}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-\beta q^{7}+q^{8}+q^{10}+\cdots\)
2574.2.a.bg 2574.a 1.a $2$ $20.553$ \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(3\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
2574.2.a.bh 2574.a 1.a $3$ $20.553$ 3.3.316.1 None \(-3\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
2574.2.a.bi 2574.a 1.a $3$ $20.553$ 3.3.961.1 None \(3\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2574.2.a.bj 2574.a 1.a $3$ $20.553$ 3.3.316.1 None \(3\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2574))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2574)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1287))\)\(^{\oplus 2}\)