Properties

Label 5415.2.a
Level $5415$
Weight $2$
Character orbit 5415.a
Rep. character $\chi_{5415}(1,\cdot)$
Character field $\Q$
Dimension $228$
Newform subspaces $46$
Sturm bound $1520$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5415.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1520\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5415))\).

Total New Old
Modular forms 800 228 572
Cusp forms 721 228 493
Eisenstein series 79 0 79

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

\(3\)\(5\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(27\)
\(+\)\(+\)\(-\)$-$\(30\)
\(+\)\(-\)\(+\)$-$\(35\)
\(+\)\(-\)\(-\)$+$\(21\)
\(-\)\(+\)\(+\)$-$\(30\)
\(-\)\(+\)\(-\)$+$\(27\)
\(-\)\(-\)\(+\)$+$\(22\)
\(-\)\(-\)\(-\)$-$\(36\)
Plus space\(+\)\(97\)
Minus space\(-\)\(131\)

Trace form

\( 228 q - 4 q^{2} + 2 q^{3} + 228 q^{4} + 2 q^{6} - 12 q^{8} + 228 q^{9} + O(q^{10}) \) \( 228 q - 4 q^{2} + 2 q^{3} + 228 q^{4} + 2 q^{6} - 12 q^{8} + 228 q^{9} + 4 q^{10} - 8 q^{11} + 6 q^{12} + 8 q^{13} + 2 q^{15} + 220 q^{16} + 8 q^{17} - 4 q^{18} - 8 q^{20} + 8 q^{21} - 8 q^{22} - 6 q^{24} + 228 q^{25} + 24 q^{26} + 2 q^{27} + 8 q^{28} - 8 q^{29} - 2 q^{30} + 12 q^{32} + 8 q^{34} + 228 q^{36} + 8 q^{37} + 4 q^{39} + 12 q^{40} + 8 q^{41} - 8 q^{42} - 24 q^{43} - 16 q^{44} + 32 q^{46} - 16 q^{47} + 30 q^{48} + 260 q^{49} - 4 q^{50} - 12 q^{51} + 40 q^{52} + 2 q^{54} - 16 q^{55} + 48 q^{56} + 48 q^{58} - 48 q^{59} + 6 q^{60} + 32 q^{61} + 80 q^{62} + 236 q^{64} + 8 q^{65} + 32 q^{66} - 24 q^{67} + 96 q^{68} + 8 q^{69} + 8 q^{70} - 16 q^{71} - 12 q^{72} + 8 q^{73} + 40 q^{74} + 2 q^{75} - 8 q^{77} + 4 q^{78} + 228 q^{81} + 40 q^{82} - 16 q^{83} + 8 q^{84} - 12 q^{87} - 8 q^{88} + 24 q^{89} + 4 q^{90} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 48 q^{94} + 10 q^{96} + 56 q^{97} - 36 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5415))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 19
5415.2.a.a 5415.a 1.a $1$ $43.239$ \(\Q\) None \(-2\) \(-1\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.b 5415.a 1.a $1$ $43.239$ \(\Q\) None \(-2\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.c 5415.a 1.a $1$ $43.239$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5415.2.a.d 5415.a 1.a $1$ $43.239$ \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5415.2.a.e 5415.a 1.a $1$ $43.239$ \(\Q\) None \(-1\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5415.2.a.f 5415.a 1.a $1$ $43.239$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
5415.2.a.g 5415.a 1.a $1$ $43.239$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
5415.2.a.h 5415.a 1.a $1$ $43.239$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5415.2.a.i 5415.a 1.a $1$ $43.239$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5415.2.a.j 5415.a 1.a $1$ $43.239$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
5415.2.a.k 5415.a 1.a $1$ $43.239$ \(\Q\) None \(2\) \(1\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.l 5415.a 1.a $1$ $43.239$ \(\Q\) None \(2\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.m 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.n 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.o 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.p 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.q 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(-2\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
5415.2.a.r 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.s 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+5q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.t 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-2\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
5415.2.a.u 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.v 5415.a 1.a $2$ $43.239$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.w 5415.a 1.a $3$ $43.239$ 3.3.148.1 None \(-1\) \(3\) \(3\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5415.2.a.x 5415.a 1.a $3$ $43.239$ 3.3.148.1 None \(1\) \(-3\) \(3\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5415.2.a.y 5415.a 1.a $5$ $43.239$ 5.5.8797896.1 None \(-1\) \(-5\) \(5\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.z 5415.a 1.a $5$ $43.239$ 5.5.8797896.1 None \(1\) \(5\) \(5\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.ba 5415.a 1.a $6$ $43.239$ 6.6.966125.1 None \(-3\) \(-6\) \(6\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{2}-q^{3}+(2-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bb 5415.a 1.a $6$ $43.239$ 6.6.1397493.1 None \(-3\) \(6\) \(6\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{5})q^{2}+q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bc 5415.a 1.a $6$ $43.239$ 6.6.5061125.1 None \(-3\) \(6\) \(-6\) \(6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5415.2.a.bd 5415.a 1.a $6$ $43.239$ 6.6.2591125.1 None \(-1\) \(-6\) \(6\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5415.2.a.be 5415.a 1.a $6$ $43.239$ 6.6.5516125.1 None \(-1\) \(6\) \(-6\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
5415.2.a.bf 5415.a 1.a $6$ $43.239$ 6.6.5516125.1 None \(1\) \(-6\) \(-6\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
5415.2.a.bg 5415.a 1.a $6$ $43.239$ 6.6.2591125.1 None \(1\) \(6\) \(6\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5415.2.a.bh 5415.a 1.a $6$ $43.239$ 6.6.1397493.1 None \(3\) \(-6\) \(6\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{5})q^{2}-q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bi 5415.a 1.a $6$ $43.239$ 6.6.5061125.1 None \(3\) \(-6\) \(-6\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bj 5415.a 1.a $6$ $43.239$ 6.6.966125.1 None \(3\) \(6\) \(6\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{2}+q^{3}+(2-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
5415.2.a.bk 5415.a 1.a $9$ $43.239$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(9\) \(-9\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
5415.2.a.bl 5415.a 1.a $9$ $43.239$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-9\) \(-9\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
5415.2.a.bm 5415.a 1.a $12$ $43.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-12\) \(-12\) \(-10\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{9}q^{2}-q^{3}+(1+\beta _{7}-\beta _{9})q^{4}-q^{5}+\cdots\)
5415.2.a.bn 5415.a 1.a $12$ $43.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(12\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+q^{5}+\cdots\)
5415.2.a.bo 5415.a 1.a $12$ $43.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-12\) \(-12\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bp 5415.a 1.a $12$ $43.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(12\) \(-12\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bq 5415.a 1.a $12$ $43.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(-12\) \(12\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+q^{5}+\cdots\)
5415.2.a.br 5415.a 1.a $12$ $43.239$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(12\) \(-12\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{9}q^{2}+q^{3}+(1+\beta _{7}-\beta _{9})q^{4}-q^{5}+\cdots\)
5415.2.a.bs 5415.a 1.a $15$ $43.239$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-3\) \(-15\) \(15\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bt 5415.a 1.a $15$ $43.239$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(3\) \(15\) \(15\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5415))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5415)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\)\(^{\oplus 2}\)