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Properties

Label 7254.2.a
Level $7254$
Weight $2$
Character orbit 7254.a
Rep. character $\chi_{7254}(1,\cdot)$
Character field $\Q$
Dimension $150$
Newform subspaces $45$
Sturm bound $2688$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 7254 = 2 \cdot 3^{2} \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7254.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(2688\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7254))\).

Total New Old
Modular forms 1360 150 1210
Cusp forms 1329 150 1179
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.

\(2\)\(3\)\(13\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(8\)
\(+\)\(+\)\(+\)\(-\)$-$\(7\)
\(+\)\(+\)\(-\)\(+\)$-$\(7\)
\(+\)\(+\)\(-\)\(-\)$+$\(8\)
\(+\)\(-\)\(+\)\(+\)$-$\(13\)
\(+\)\(-\)\(+\)\(-\)$+$\(10\)
\(+\)\(-\)\(-\)\(+\)$+$\(10\)
\(+\)\(-\)\(-\)\(-\)$-$\(13\)
\(-\)\(+\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(+\)\(-\)$+$\(7\)
\(-\)\(+\)\(-\)\(+\)$+$\(7\)
\(-\)\(+\)\(-\)\(-\)$-$\(8\)
\(-\)\(-\)\(+\)\(+\)$+$\(9\)
\(-\)\(-\)\(+\)\(-\)$-$\(13\)
\(-\)\(-\)\(-\)\(+\)$-$\(13\)
\(-\)\(-\)\(-\)\(-\)$+$\(9\)
Plus space\(+\)\(68\)
Minus space\(-\)\(82\)

Trace form

\( 150 q - 2 q^{2} + 150 q^{4} + 4 q^{5} + 8 q^{7} - 2 q^{8} + O(q^{10}) \) \( 150 q - 2 q^{2} + 150 q^{4} + 4 q^{5} + 8 q^{7} - 2 q^{8} + 4 q^{11} - 8 q^{14} + 150 q^{16} - 12 q^{17} + 24 q^{19} + 4 q^{20} + 12 q^{22} + 16 q^{23} + 158 q^{25} + 8 q^{28} - 2 q^{32} - 4 q^{34} - 8 q^{35} - 8 q^{37} - 4 q^{38} - 20 q^{41} + 28 q^{43} + 4 q^{44} + 24 q^{46} + 40 q^{47} + 166 q^{49} - 46 q^{50} + 24 q^{53} - 32 q^{55} - 8 q^{56} - 16 q^{58} - 56 q^{59} - 8 q^{61} + 150 q^{64} - 16 q^{67} - 12 q^{68} + 32 q^{70} + 8 q^{71} + 12 q^{73} + 16 q^{74} + 24 q^{76} - 48 q^{77} + 4 q^{80} - 12 q^{82} + 44 q^{83} - 16 q^{85} - 20 q^{86} + 12 q^{88} + 36 q^{89} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{95} + 4 q^{97} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7254))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 13 31
7254.2.a.a 7254.a 1.a $1$ $57.923$ \(\Q\) None 2418.2.a.c \(-1\) \(0\) \(-4\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}+3q^{7}-q^{8}+4q^{10}+\cdots\)
7254.2.a.b 7254.a 1.a $1$ $57.923$ \(\Q\) None 806.2.a.f \(-1\) \(0\) \(-3\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
7254.2.a.c 7254.a 1.a $1$ $57.923$ \(\Q\) None 7254.2.a.c \(-1\) \(0\) \(-2\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+3q^{7}-q^{8}+2q^{10}+\cdots\)
7254.2.a.d 7254.a 1.a $1$ $57.923$ \(\Q\) None 806.2.a.c \(-1\) \(0\) \(-1\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
7254.2.a.e 7254.a 1.a $1$ $57.923$ \(\Q\) None 806.2.a.d \(-1\) \(0\) \(-1\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots\)
7254.2.a.f 7254.a 1.a $1$ $57.923$ \(\Q\) None 7254.2.a.f \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-2q^{11}+\cdots\)
7254.2.a.g 7254.a 1.a $1$ $57.923$ \(\Q\) None 7254.2.a.g \(-1\) \(0\) \(2\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+3q^{7}-q^{8}-2q^{10}+\cdots\)
7254.2.a.h 7254.a 1.a $1$ $57.923$ \(\Q\) None 806.2.a.e \(-1\) \(0\) \(3\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots\)
7254.2.a.i 7254.a 1.a $1$ $57.923$ \(\Q\) None 7254.2.a.f \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+2q^{11}+\cdots\)
7254.2.a.j 7254.a 1.a $1$ $57.923$ \(\Q\) None 7254.2.a.g \(1\) \(0\) \(-2\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+3q^{7}+q^{8}-2q^{10}+\cdots\)
7254.2.a.k 7254.a 1.a $1$ $57.923$ \(\Q\) None 806.2.a.b \(1\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots\)
7254.2.a.l 7254.a 1.a $1$ $57.923$ \(\Q\) None 2418.2.a.a \(1\) \(0\) \(0\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{7}+q^{8}+4q^{11}-q^{13}+\cdots\)
7254.2.a.m 7254.a 1.a $1$ $57.923$ \(\Q\) None 2418.2.a.b \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
7254.2.a.n 7254.a 1.a $1$ $57.923$ \(\Q\) None 806.2.a.a \(1\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
7254.2.a.o 7254.a 1.a $1$ $57.923$ \(\Q\) None 7254.2.a.c \(1\) \(0\) \(2\) \(3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+3q^{7}+q^{8}+2q^{10}+\cdots\)
7254.2.a.p 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{5}) \) None 806.2.a.h \(-2\) \(0\) \(0\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta q^{5}+(-2-\beta )q^{7}-q^{8}+\cdots\)
7254.2.a.q 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{5}) \) None 2418.2.a.g \(-2\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-\beta q^{7}-q^{8}-\beta q^{10}+\cdots\)
7254.2.a.r 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{5}) \) None 2418.2.a.i \(-2\) \(0\) \(3\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}+(-3+3\beta )q^{7}+\cdots\)
7254.2.a.s 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{5}) \) None 2418.2.a.f \(-2\) \(0\) \(3\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
7254.2.a.t 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{13}) \) None 2418.2.a.h \(-2\) \(0\) \(5\) \(-3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(3-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
7254.2.a.u 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{5}) \) None 2418.2.a.e \(2\) \(0\) \(-5\) \(3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2-\beta )q^{5}+(2-\beta )q^{7}+\cdots\)
7254.2.a.v 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{21}) \) None 2418.2.a.d \(2\) \(0\) \(1\) \(3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+(2-\beta )q^{7}+q^{8}+\cdots\)
7254.2.a.w 7254.a 1.a $2$ $57.923$ \(\Q(\sqrt{5}) \) None 806.2.a.g \(2\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(-2-\beta )q^{7}+q^{8}+\cdots\)
7254.2.a.x 7254.a 1.a $3$ $57.923$ \(\Q(\zeta_{14})^+\) None 806.2.a.i \(-3\) \(0\) \(5\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2-\beta _{1})q^{5}+(2+2\beta _{2})q^{7}+\cdots\)
7254.2.a.y 7254.a 1.a $3$ $57.923$ 3.3.733.1 None 2418.2.a.j \(3\) \(0\) \(3\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7254.2.a.z 7254.a 1.a $4$ $57.923$ 4.4.22896.1 None 2418.2.a.m \(4\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
7254.2.a.ba 7254.a 1.a $4$ $57.923$ 4.4.18736.1 None 2418.2.a.l \(4\) \(0\) \(0\) \(-10\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+(-3+\cdots)q^{7}+\cdots\)
7254.2.a.bb 7254.a 1.a $4$ $57.923$ 4.4.5744.1 None 2418.2.a.n \(4\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{8}+\cdots\)
7254.2.a.bc 7254.a 1.a $4$ $57.923$ 4.4.24197.1 None 2418.2.a.k \(4\) \(0\) \(3\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{3})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
7254.2.a.bd 7254.a 1.a $5$ $57.923$ 5.5.17108032.1 None 2418.2.a.p \(-5\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{2}q^{5}+\beta _{4}q^{7}-q^{8}+\cdots\)
7254.2.a.be 7254.a 1.a $5$ $57.923$ 5.5.25175056.1 None 2418.2.a.q \(-5\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+\cdots\)
7254.2.a.bf 7254.a 1.a $5$ $57.923$ 5.5.1772453.1 None 806.2.a.j \(5\) \(0\) \(-5\) \(8\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}+(2+\beta _{3}+\cdots)q^{7}+\cdots\)
7254.2.a.bg 7254.a 1.a $5$ $57.923$ 5.5.170701.1 None 806.2.a.k \(5\) \(0\) \(-3\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
7254.2.a.bh 7254.a 1.a $5$ $57.923$ 5.5.2240944.1 None 2418.2.a.o \(5\) \(0\) \(6\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7254.2.a.bi 7254.a 1.a $6$ $57.923$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 2418.2.a.s \(-6\) \(0\) \(-6\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots\)
7254.2.a.bj 7254.a 1.a $6$ $57.923$ 6.6.927667520.1 None 2418.2.a.r \(-6\) \(0\) \(-4\) \(5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
7254.2.a.bk 7254.a 1.a $6$ $57.923$ 6.6.58446133.1 None 806.2.a.l \(-6\) \(0\) \(-3\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{3}q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7254.2.a.bl 7254.a 1.a $6$ $57.923$ 6.6.476177744.1 None 7254.2.a.bl \(-6\) \(0\) \(5\) \(-7\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7254.2.a.bm 7254.a 1.a $6$ $57.923$ 6.6.476177744.1 None 7254.2.a.bl \(6\) \(0\) \(-5\) \(-7\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7254.2.a.bn 7254.a 1.a $7$ $57.923$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 7254.2.a.bn \(-7\) \(0\) \(-9\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
7254.2.a.bo 7254.a 1.a $7$ $57.923$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 7254.2.a.bo \(-7\) \(0\) \(-1\) \(5\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(\beta _{1}+\beta _{5}+\beta _{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
7254.2.a.bp 7254.a 1.a $7$ $57.923$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 7254.2.a.bp \(-7\) \(0\) \(3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{5}q^{5}+(-\beta _{1}-\beta _{4})q^{7}+\cdots\)
7254.2.a.bq 7254.a 1.a $7$ $57.923$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 7254.2.a.bp \(7\) \(0\) \(-3\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{5}q^{5}+(-\beta _{1}-\beta _{4})q^{7}+\cdots\)
7254.2.a.br 7254.a 1.a $7$ $57.923$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 7254.2.a.bo \(7\) \(0\) \(1\) \(5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{5}-\beta _{6})q^{5}+\cdots\)
7254.2.a.bs 7254.a 1.a $7$ $57.923$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 7254.2.a.bn \(7\) \(0\) \(9\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{1})q^{5}+(1+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7254))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7254)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(403))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(806))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3627))\)\(^{\oplus 2}\)